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Transcript of Chapter 12 Resource Masters - Math Problem Solving - …©Glencoe/McGraw-Hill v Glencoe Geometry...
Chapter 12Resource Masters
Geometry
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.
Study Guide and Intervention Workbook 0-07-860191-6Skills Practice Workbook 0-07-860192-4Practice Workbook 0-07-860193-2Reading to Learn Mathematics Workbook 0-07-861061-3
ANSWERS FOR WORKBOOKS The answers for Chapter 12 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-860189-4 GeometryChapter 12 Resource Masters
1 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03
© Glencoe/McGraw-Hill iii Glencoe Geometry
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 12-1Study Guide and Intervention . . . . . . . . 661–662Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 663Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 664Reading to Learn Mathematics . . . . . . . . . . 665Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 666
Lesson 12-2Study Guide and Intervention . . . . . . . . 667–668Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 669Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 670Reading to Learn Mathematics . . . . . . . . . . 671Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 672
Lesson 12-3Study Guide and Intervention . . . . . . . . 673–674Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 675Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 676Reading to Learn Mathematics . . . . . . . . . . 677Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 678
Lesson 12-4Study Guide and Intervention . . . . . . . . 679–680Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 681Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 682Reading to Learn Mathematics . . . . . . . . . . 683Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 684
Lesson 12-5Study Guide and Intervention . . . . . . . . 685–686Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 687Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 688Reading to Learn Mathematics . . . . . . . . . . 689Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 690
Lesson 12-6Study Guide and Intervention . . . . . . . . 691–692Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 693Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 694Reading to Learn Mathematics . . . . . . . . . . 695Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 696
Lesson 12-7Study Guide and Intervention . . . . . . . . 697–698Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 699Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 700Reading to Learn Mathematics . . . . . . . . . . 701Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 702
Chapter 12 AssessmentChapter 12 Test, Form 1 . . . . . . . . . . . 703–704Chapter 12 Test, Form 2A . . . . . . . . . . 705–706Chapter 12 Test, Form 2B . . . . . . . . . . 707–708Chapter 12 Test, Form 2C . . . . . . . . . . 709–710Chapter 12 Test, Form 2D . . . . . . . . . . 711–712Chapter 12 Test, Form 3 . . . . . . . . . . . 713–714Chapter 12 Open-Ended Assessment . . . . . 715Chapter 12 Vocabulary Test/Review . . . . . . 716Chapter 12 Quizzes 1 & 2 . . . . . . . . . . . . . . 717Chapter 12 Quizzes 3 & 4 . . . . . . . . . . . . . . 718Chapter 12 Mid-Chapter Test . . . . . . . . . . . . 719Chapter 12 Cumulative Review . . . . . . . . . . 720Chapter 12 Standardized Test Practice 721–722
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32
© Glencoe/McGraw-Hill iv Glencoe Geometry
Teacher’s Guide to Using theChapter 12 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 12 Resource Masters includes the core materialsneeded for Chapter 12. These materials include worksheets, extensions, andassessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGeometry TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 12-1.Encourage them to add these pages to theirGeometry Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Geometry addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Geometry
Assessment OptionsThe assessment masters in the Chapter 12Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Geometry. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of geometry conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and short-responsequestions. Bubble-in and grid-in answersections are provided on the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 684–685. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
1212
© Glencoe/McGraw-Hill vii Glencoe Geometry
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 12. As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
altitude
axis
cone
cylinder
great circle
hemisphere
lateral area
lateral edges
lateral faces
net
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Geometry
Vocabulary Term Found on Page Definition/Description/Example
oblique
orthogonal drawing
ohr·THAHG·uhn·uhl
polyhedrons
prism
PRIZ·uhm
pyramid
regular polyhedron
regular prism
right
sphere
SFIR
surface area
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
1212
Study Guide and InterventionThree-Dimensional Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 661 Glencoe Geometry
Less
on
12-
1
Drawings of Three-Dimensional Figures To work with a three-dimensionalobject, a useful skill is the ability to make an orthogonal drawing, which is a set of two-dimensional drawings of the different sides of the object. For a square pyramid, you wouldshow the top view, the left view, the front view, and the right view.
Draw the back view of the figure given the orthogonal drawing.• The top view indicates two columns.• The left view indicates that the height of figure is
three blocks.• The front view indicates that the columns have heights 2 and 3 blocks.• The right view indicates that the height of the figure is three blocks.
Use blocks to make a model of the object. Then use your model to draw the back view. The back view indicates that the columns have heights 3 and 2 blocks.
Draw the back view and corner view of a figure given each orthogonal drawing.
1. 2.
3. 4.
back viewcorner view
top view left view front view right view
back viewcorner view
top view left view front view right view
back viewcorner view
top view left view front view right view
back viewcorner view
top view left view front view right view
back viewobject
top view left view front view right view
object top view left view front view right view
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 662 Glencoe Geometry
Identify Three-Dimensional Figures A polyhedron is a solid with all flatsurfaces. Each surface of a polyhedron is called a face, and each line segment where facesintersect is called an edge. Two special kinds of polyhedra are prisms, for which two facesare congruent, parallel bases, and pyramids, for which one face is a base and all the otherfaces meet at a point called the vertex. Prisms and pyramids are named for the shape oftheir bases, and a regular polyhedron has a regular polygon as its base.
Other solids are a cylinder, which has congruent circular bases in parallel planes, a cone,which has one circular base and a vertex, and a sphere.
Identify each solid. Name the bases, faces, edges, and vertices.
pentagonalprism
squarepyramid
pentagonalpyramid
rectangularprism
sphereconecylinder
Study Guide and Intervention (continued)
Three-Dimensional Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
ExampleExamplea.
The figure is a rectangular pyramid. The base isrectangle ABCD, and the four faces �ABE, �BCE,�CDE, and �ADE meet at vertex E. The edges areA�B�, B�C�, C�D�, A�D�, A�E�, B�E�, C�E�, and D�E�. The verticesare A, B, C, D, and E.
E
A B
CD
b.
This solid is a cylinder. Thetwo bases are �O and �P.
P
O
ExercisesExercises
Identify each solid. Name the bases, faces, edges, and vertices.
1. 2.
3. 4.
A B
CF
D E
P WQ
VZ X
U
SR
Y
T
S
R
Skills PracticeThree-Dimensional Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 663 Glencoe Geometry
Less
on
12-
1
Draw the back view and corner view of a figure given each orthogonal drawing.
1. 2.
Identify each solid. Name the bases, faces, edges, and vertices.
3.
4.
5.
S
R
F
AB C
DE
U T
WV
R S
XY
back view corner view
top view left view front view right view
back view corner view
top view left view front view right view
© Glencoe/McGraw-Hill 664 Glencoe Geometry
Draw the back view and corner view of a figure given each orthogonal drawing.
1. 2.
Identify each solid. Name the bases, faces, edges, and vertices.
3.
4.
5. MINERALS Pyrite, also known as fool’s gold, can form crystals that are perfect cubes.Suppose a gemologist wants to cut a cube of pyrite to get a square and a rectangularface. What cuts should be made to get each of the shapes? Illustrate your answers.
Z
T
I J
MH K
N
O L
back view corner view
top view left view front view right view
back view corner view
top view left view front view right view
Practice Three-Dimensional Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
Reading to Learn MathematicsThree-Dimensional Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 665 Glencoe Geometry
Less
on
12-
1
Pre-Activity Why are drawings of three-dimensional structures valuable toarcheologists?
Read the introduction to Lesson 12-1 at the top of page 636 in your textbook.
Why do you think archeologists would want to know the details of the sizesand shapes of ancient three-dimensional structures?
Reading the Lesson1. Match each description from the first column with one of the terms from the second
column. (Some of the terms may be used more than once or not at all.)
a. a polyhedron with two parallel congruent basesb. the set of points in space that are a given distance from a
given pointc. a regular polyhedron with eight facesd. a polyhedron that has all faces but one intersecting at one
pointe. a line segment where two faces of a polyhedron intersectf. a solid with congruent circular bases in a pair of parallel
planesg. a regular polyhedron whose faces are squaresh. a flat surface of a polyhedron
i. octahedronii. face
iii. icosahedroniv. edgev. prism
vi. dodecahedronvii. cylinderviii. sphereix. conex. hexahedron
xi. pyramidxii. tetrahedron
2. Fill in the missing numbers, words, or phrases to complete each sentence.
a. A triangular prism has vertices. It has faces: bases are congruent
, and faces are parallelograms.
b. A regular octahedron has vertices and faces. Each face is a(n)
.
c. A hexagonal prism has vertices. It has faces: of them are the bases,
which are congruent , and the other faces are parallelograms.
d. An octagonal pyramid has vertices and faces. The base is a(n)
, and the other faces are .
e. There are exactly types of regular polyhedra. These are called the
solids. A polyhedron whose faces are regular pentagons is a
, which has faces.
Helping You Remember3. A good way to remember the characteristics of geometric solids is to think about how
different solids are alike. Name a way in which pyramids and cones are alike.
© Glencoe/McGraw-Hill 666 Glencoe Geometry
Drawing Solids on Isometric Dot PaperIsometric dot paper is helpful for drawing solids. Remember to usedashed lines for hidden edges.
For each solid shown, draw another solid whose dimensions are twice as large.
1. 2.
3. 4.
5. 6.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
Study Guide and InterventionNets and Surface Area
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 667 Glencoe Geometry
Less
on
12-
2
Models for Three-Dimensional Figures One way to relate a three-dimensionalfigure and a two-dimensional drawing is to use isometric dot paper. Another way is to makea flat pattern, called a net, for the surfaces of a solid.
Use isometric dot paper to sketch a triangular prism with 3-4-5 right triangles as bases and with a height of 3 units.Step 1 Draw A�B� at 3 units and draw A�C� at 4 units.Step 2 Draw A�D�, B�E�, and C�F�, each at 3 units.Step 3 Draw B�C� and �DEF.
Match the net at the right with one of the solids below.
The six squares of the net can be folded into a cube. The net represents solid c.
Sketch each solid using isometric dot paper.
1. cube with edge 4 2. rectangular prism 1 unit high, 5 unitslong, and 4 units wide
Draw a net for each solid.
3. 4.
5. 6.
c.b.a.
A
B CD
E F
ExercisesExercises
Example 1Example 1
Example 2Example 2
© Glencoe/McGraw-Hill 668 Glencoe Geometry
Surface Area The surface area of a solid is the sum of the areas of the faces of thesolid. Nets are useful in visualizing each face and calculating the area of the faces.
Find the surface area of the triangular prism.
First draw a net using rectangular dot paper. Using the Pythagorean Theorem,
the hypotenuse of the right triangle is �32 � 4�2� or 5.
Surface area � A � B � C � D � E
� �12�(4 � 3) � 4 � 4 � 4 � 3 � 4 � 5 � �
12�(4 � 3)
� 60 square units
Find the surface area of each solid. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
4025
2020
1518
88
10
9126
5 m5 m
5 m
24 cm5 cm
10 cm
12 in.8 in.
5 in.
A
C
E
B D4
43
Study Guide and Intervention (continued)
Nets and Surface Area
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
ExercisesExercises
ExampleExample
Skills PracticeNets and Surface Area
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 669 Glencoe Geometry
Less
on
12-
2
Sketch each solid using isometric dot paper.
1. cube 2 units on each edge 2. rectangular prism 2 units high,5 units long, and 2 units wide
For each solid, draw a net and find the surface area.
3.
4.
55
6
7
3
5
© Glencoe/McGraw-Hill 670 Glencoe Geometry
Sketch each solid using isometric dot paper.
1. rectangular prism 3 units high, 2. triangular prism 3 units high, whose bases 3 units long, and 2 units wide are right triangles with legs 2 units and
4 units long
3. For the solid, draw a net and find the surface area.
4. SHIPPING Rawanda needs to wrap a package to ship to her aunt. The rectangularpackage measures 2 inches high, 10 inches long, and 4 inches wide. Draw a net of thepackage. How much wrapping paper does Rawanda need to cover the package?
2
10
2
4
3
96
15
Practice Nets and Surface Area
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
Reading to Learn MathematicsNets and Surface Area
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 671 Glencoe Geometry
Less
on
12-
2
Pre-Activity Why is surface area important to car manufacturers?
Read the introduction to Lesson 12-2 at the top of page 643 in your textbook.
Suppose you are a passenger in a car that is moving at 50 miles per hour onthe highway. If you hold your right hand just outside the right window, inwhat position does your hand encounter the greatest air resistance?
Reading the Lesson
1. Name the solid that can be formed by folding each net without any overlap.
a. b.
c. d.
2. Supply the missing number, word, or phrase to make a true statement. Be as specific aspossible.
a. To find the surface area of a cube, add the areas of congruent squares.
b. To find the surface area of a cylinder, add the areas of two congruent
and one .
c. To find the surface area of a dodecahedron, add the areas of 12 congruent
.
d. To find the surface area of an icosahedron, add the areas of congruent
triangles.
Helping You Remember
3. A good way to remember a mathematical concept is to think about how the conceptrelates to everyday life. How could you explain the concept of surface area using aneveryday situation?
© Glencoe/McGraw-Hill 672 Glencoe Geometry
Pyramids
1. On a sheet of paper, draw the figure at the right so that the measurements are accurate.Cut out the shape and fold it to make a pyramid.
2. Measure the height from the highest point straight down (perpendicular) to the base.What is the height of the pyramid?
The drawing at the right shows the pyramid you made.Answer each of the following.
3. Measure the length of y in your pyramid.
4. Measure the length of z, the height of one of the triangular faces.
5. Use the Pythagorean Theorem to find x, the height of the pyramid.Is this equal to the height of your model?
Make a paper pattern for each pyramid below. Cut out your pattern and fold it tomake a model. Measure the height of the pyramid and use the PythagoreanTheorem to verify this measure.
6. 7.
12.5 cm
7 cm
5 cm
8 cm
y
x z
10 cm
13cm
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
Study Guide and InterventionSurface Areas of Prisms
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 673 Glencoe Geometry
Less
on
12-
3
Lateral Areas of Prisms Here are some characteristics of prisms.
• The bases are parallel and congruent.• The lateral faces are the faces that are not bases.• The lateral faces intersect at lateral edges, which are parallel.• The altitude of a prism is a segment that is perpendicular
to the bases with an endpoint in each base.• For a right prism, the lateral edges are perpendicular to the
bases. Otherwise, the prism is oblique.
Lateral Area If a prism has a lateral area of L square units, a height of h units, of a Prism and each base has a perimeter of P units, then L � Ph.
Find the lateral area of the regular pentagonal prism above if eachbase has a perimeter of 75 centimeters and the altitude is 10 centimeters.L � Ph Lateral area of a prism
� 75(10) P � 75, h � 10
� 750 Multiply.
The lateral area is 750 square centimeters.
Find the lateral area of each prism.
1. 2.
3. 4.
5. 6.
4 m16 m
4 in.
4 in.
12 in.
20 cm
10 cm 10 cm
12 cm9 cm
6 in.18 in.
15 in.
10 in.
8 in.4 m
3 m10 m
pentagonal prism
altitude
lateraledge lateral
face
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 674 Glencoe Geometry
Surface Areas of Prisms The surface area of a prism is thelateral area of the prism plus the areas of the bases.
Surface AreaIf the total surface area of a prism is T square units, its height is
of a Prismh units, and each base has an area of B square units and a perimeter of P units, then T � L � 2B.
Find the surface area of the triangular prism above.Find the lateral area of the prism.
L � Ph Lateral area of a prism
� (18)(10) P � 18, h � 10
� 180 cm2 Multiply.
Find the area of each base. Use the Pythagorean Theorem to find the height of thetriangular base.
h2 � 32 � 62 Pythagorean Theorem
h2 � 27 Simplify.
h � 3�3� Take the square root of each side.
B � �12� � base � height Area of a triangle
� �12�(6)(3�3�) or 15.6 cm2
The total area is the lateral area plus the area of the two bases.
T � 180 � 2(15.6) Substitution
� 211.2 cm2 Simplify.
Find the surface area of each prism. Round to the nearest tenth if necessary.
1. 2. 3.
4. 5. 6.
8 m
8 m8 m
8 in.
8 in.
8 in.
15 in.6 in.
12 in.
12 m
5 m6 m
3 m6 m
4 m
24 in.
10 in.
8 in.
6 cm
6 cm
6 cm
10 cmh
Study Guide and Intervention (continued)
Surface Areas of Prisms
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
ExercisesExercises
ExampleExample
Skills PracticeSurface Areas of Prisms
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 675 Glencoe Geometry
Less
on
12-
3
Find the lateral area of each prism.
1. 2.
3. 4.
Find the surface area of each prism. Round to the nearest tenth if necessary.
5. 6.
7. 8.
7
4
39
610
15
7
13
18
8
6
9
9
9
12
105
6
8
8
6
12
12
12
10
© Glencoe/McGraw-Hill 676 Glencoe Geometry
Find the lateral area of each prism. Round to the nearest tenth if necessary.
1. 2.
3. 4.
Find the surface area of each prism. Round to the nearest tenth if necessary.
5. 6.
7. 8.
9. CRAFTS Becca made a rectangular jewelry box in her art class and plans to cover it in red
silk. If the jewelry box is 6�12� inches long, 4 �
12� inches wide, and 3 inches high, find the
surface area that will be covered.
14
14
23
9
95
6
13
79
4
17
4
4
9.5
52
11
8
105
15
15
32
Practice Surface Areas of Prisms
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
Reading to Learn MathematicsSurface Areas of Prisms
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 677 Glencoe Geometry
Less
on
12-
3
Pre-Activity How do brick masons know how many bricks to order for a project?
Read the introduction to Lesson 12-3 at the top of page 649 in your textbook.
How could the brick mason figure out approximately how many bricks areneeded for the garage?
Reading the Lesson1. Determine whether each sentence is always, sometimes, or never true.
a. A base of a prism is a face of the prism.b. A face of a prism is a base of the prism.c. The lateral faces of a prism are rectangles.d. If a base of a prism has n vertices, then the prism has n faces.e. If a base of a prism has n vertices, then the prism has n lateral edges.f. In a right prism, the lateral edges are also altitudes.g. The bases of a prism are congruent regular polygons.h. Any two lateral edges of a prism are perpendicular to each other.i. In a rectangular prism, any pair of opposite faces can be called the bases.j. All of the lateral faces of a prism are congruent to each other.
2. Explain the difference between the lateral area of a prism and the surface area of aprism. Your explanation should apply to both right and oblique prisms. Do not use anyformulas in your explanation.
3. Refer to the figure.
a. Name this solid with as specific a name as possible.
b. Name the bases of the solid.c. Name the lateral faces.
d. Name the edges.e. Name an altitude of the solid.f. If a represents the area, P represents the perimeter of one of the bases, and x � AF,
write an expression for the surface area of the solid that involves a, P, and x.
Helping You Remember4. A good way to remember a new mathematical term is to relate it to an everyday use of
the same word. How can the way the word lateral is used in sports help you rememberthe meaning of the lateral area of a solid?
A
B C
D
IF
E
G H
J
© Glencoe/McGraw-Hill 678 Glencoe Geometry
Cross Sections of PrismsWhen a plane intersects a solid figure to form a two-dimensional figure, the results is called a cross section. The figure at the right shows a plane intersecting a cube. The cross section is a hexagon.
For each right prism, connect the labeled points in alphabetical order to show a cross section. Then identify the polygon.
1. 2. 3.
Refer to the right prisms shown at the right. In the rectangular prism, A and Care midpoints. Identify the cross-section polygon formed by a plane containing the given points.
4. A, C, H
5. C, E, G
6. H, C, E, F
7. H, A, E
8. B, D, F
9. V, X, R
10. R, T, Y
11. R, S, W
A
B
H G
F
DC
E
V X
SU
Y
Z
R
T
W
A B
CD
X
Y
Z
S
R
U
T
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
Study Guide and InterventionSurface Areas of Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 679 Glencoe Geometry
Less
on
12-
4
Lateral Areas of Cylinders A cylinder is a solid whose bases are congruent circles that lie in parallel planes. The axisof a cylinder is the segment whose endpoints are the centers of these circles. For a right cylinder, the axis and the altitude of the cylinder are equal. The lateral area of a right cylinder is thecircumference of the cylinder multiplied by the height.
Lateral Area If a cylinder has a lateral area of L square units, a height of h units, of a Cylinder and the bases have radii of r units, then L � 2�rh.
Find the lateral area of the cylinder above if the radius of the baseis 6 centimeters and the height is 14 centimeters.L � 2�rh Lateral area of a cylinder
� 2�(6)(14) Substitution
� 527.8 Simplify.
The lateral area is about 527.8 square centimeters.
Find the lateral area of each cylinder. Round to the nearest tenth.
1. 2.
3. 4.
5. 6. 2 m
1 m12 m
4 m
20 cm
8 cm
6 cm
3 cm
3 cm
6 in.10 in.
12 cm
4 cm
radius of baseaxis
base
baseheight
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 680 Glencoe Geometry
Surface Areas of Cylinders The surface area of a cylinder is the lateral area of the cylinder plus the areas of the bases.
Surface Area If a cylinder has a surface area of T square units, a height of of a Cylinder h units, and the bases have radii of r units, then T � 2�rh � 2�r 2.
Find the surface area of the cylinder.Find the lateral area of the cylinder. If the diameter is 12 centimeters, then the radius is 6 centimeters.
L � Ph Lateral area of a cylinder
� (2�r)h P � 2�r
� 2�(6)(14) r � 6, h � 14
� 527.8 Simplify.
Find the area of each base.
B � �r2 Area of a circle
� �(6)2 r � 6
� 113.1 Simplify.
The total area is the lateral area plus the area of the two bases.T � 527.8 � 113.1 � 113.1 or 754 square centimeters.
Find the surface area of each cylinder. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
20 in.
8 in.
2 m 15 m
8 in.
12 in.
2 yd
3 yd
2 m
2 m
12 in.
10 in.
14 cm
12 cm
base
baselateral area
Study Guide and Intervention (continued)
Surface Areas of Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
ExercisesExercises
ExampleExample
Skills PracticeSurface Areas of Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 681 Glencoe Geometry
Less
on
12-
4
Find the surface area of a cylinder with the given dimensions. Round to thenearest tenth.
1. r � 10 in., h � 12 in. 2. r � 8 cm, h � 15 cm
3. r � 5 ft, h � 20 ft 4. d � 20 yd, h � 5 yd
5. d � 8 m, h � 7 m 6. d � 24 mm, h � 20 mm
Find the surface area of each cylinder. Round to the nearest tenth.
7. 8.
Find the radius of the base of each cylinder.
9. The surface area is 603.2 square meters, and the height is 10 meters.
10. The surface area is 100.5 square inches, and the height is 6 inches.
11. The surface area is 226.2 square centimeters, and the height is 5 centimeters.
12. The surface area is 1520.5 square yards, and the height is 14.2 yards.
4 m
8.5 m
5 ft
7 ft
© Glencoe/McGraw-Hill 682 Glencoe Geometry
Find the surface area of a cylinder with the given dimensions. Round to thenearest tenth.
1. r � 8 cm, h � 9 cm 2. r � 12 in., h � 14 in.
3. d � 14 mm, h � 32 mm 4. d � 6 yd, h � 12 yd
5. r � 2.5 ft, h � 7 ft 6. d � 13 m, h � 20 m
Find the surface area of each cylinder. Round to the nearest tenth.
7. 8.
Find the radius of the base of each right cylinder.
9. The surface area is 628.3 square millimeters, and the height is 15 millimeters.
10. The surface area is 892.2 square feet, and the height is 4.2 feet.
11. The surface area is 158.3 square inches, and the height is 5.4 inches.
12. KALEIDOSCOPES Nathan built a kaleidoscope with a 20-centimeter barrel and a 5-centimeter diameter. He plans to cover the barrel with embossed paper of his owndesign. How many square centimeters of paper will it take to cover the barrel of thekaleidoscope?
12 m30 m
19 in.
17 in.
Practice Surface Areas of Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
Reading to Learn MathematicsSurface Areas of Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 683 Glencoe Geometry
Less
on
12-
4
Pre-Activity How are cylinders used in extreme sports?Read the introduction to Lesson 12-4 at the top of page 655 in your textbook.
Why is the surface area of a half-pipe more than half the surface area of acomplete pipe?
Reading the Lesson1. Underline the correct word or phrase to form a true statement.
a. The bases of a cylinder are (rectangles/regular polygons/circles).
b. The (axis/radius/diameter) of a cylinder is the segment whose endpoints are thecenters of the bases.
c. The net of a cylinder is composed of two congruent (rectangles/circles) and one(rectangle/semicircle).
d. In a right cylinder, the axis of the cylinder is also a(n) (base/lateral edge/altitude).
e. A cylinder that is not a right cylinder is called an (acute/obtuse/oblique) cylinder.
2. Match each description from the first column with an expression from the second columnthat represents its value.a. the lateral area of a right cylinder in which the radius of
each base is x cm and the length of the axis is y cm
b. the surface area of a right prism with square bases in whichthe length of a side of a base is x cm and the length of alateral edge is y cm
c. the surface area of a right cylinder in which the radius of abase is x cm and the height is y cm
d. the surface area of regular hexahedron (cube) in which thelength of each edge is x cm
e. the lateral area of a triangular prism in which the bases areequilateral triangles with side length x cm and the height isy cm
f. the surface area of a right cylinder in which the diameter ofthe base is x cm and the length of the axis is y cm
i. (2x2 � 4xy) cm2
ii. (2�xy � 2�x2) cm2
iii. 3xy cm2
iv. 6x2 cm2
v. 2�xy cm2
vi. ���2x2� � �xy� cm2
Helping You Remember3. Often the best way to remember a mathematical formula is to think about where the
different parts of the formula come from. How can you use this approach to remember theformula for the surface area of a cylinder?
© Glencoe/McGraw-Hill 684 Glencoe Geometry
Can-didly SpeakingBeverage companies have mathematically determined the ideal shape for a 12-ounce soft-drink can. Why won't any shape do? Some shapes are moreeconomical than others. In order to hold 12 ounces of soft drink, an extremelyskinny can would have to be very tall. The total amount of aluminum used forsuch a shape would be greater than the amount used for the conventional shape,thus costing the company more to make the skinny can. The radius r chosendetermines the height h needed to hold 12 ounces of liquid. This also determinesthe amount of aluminum needed to make the can. Companies also have to keepin mind that the top of the can is three times thicker than the bottom and sides.Why? So you won’t tear off the entire top when you open the can! The followingformulas can be used to find the height and amount of aluminum a needed for a12-ounce soft-drink can.
h � �1�
7.r829
�
a � 0.02���r2 �
r35.78�� The values of r and h are measured in inches.
Find the height needed for a 12-ounce can for each radius.Round to the nearest tenth.
1. 2�23� in. 2. 1 in. 3. 3 in. 4. 1�
34� in.
Sketch the shape of each can in Exercises 1–4.
5. Exercise 1 6. Exercise 2 7. Exercise 3 8. Exercise 4
9. a. Measure the radius of a soft-drink can.
b. Use the formula to find the height of the can.
c. Measure the height of a soft-drink can.
d. How does this measure compare to your findings in part a?
10. Find the amount of aluminum used in making a soft-drink can.
13–4 in.
1.9 in.
3 in.
0.6 in.5.7 in.
1 in.22–3 in.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
Study Guide and InterventionSurface Areas of Pyramids
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 685 Glencoe Geometry
Less
on
12-
5
Lateral Areas of Regular Pyramids Here are some properties of pyramids.• The base is a polygon.• All of the faces, except the base, intersect in a common point known as the vertex.• The faces that intersect at the vertex, which are called lateral faces, are triangles.
For a regular pyramid, the base is a regular polygon and the slant height is the height of each lateral face.
Lateral Area of a If a regular pyramid has a lateral area of L square units, a slant height of � units, Regular Pyramid and its base has a perimeter of P units, then L � �1
2�P�.
The roof of a barn is a regular octagonal pyramid. The base of the pyramid has sides of 12 feet,and the slant height of the roof is 15 feet. Find the lateral area of the roof.The perimeter of the base is 8(12) or 96 feet.
L � �12�P� Lateral area of a pyramid
� �12�(96)(15) P � 96, � � 15
� 720 Multiply.
The lateral area is 720 square feet.
Find the lateral area of each regular pyramid. Round to the nearest tenth ifnecessary.
1. 2.
3. 4.
5. 6.
45� 12 yd60�18 in.
60� 6 ft
42 m
20 m
3.5 ft
10 ft
8 cm
8 cm
8 cm
15 cm
base
lateral edgelateral face
vertex
slant height
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 686 Glencoe Geometry
Surface Areas of Regular Pyramids The surface area of a regular pyramid is the lateral area plus the area of the base.
Surface Area of aIf a regular pyramid has a surface area of T square units,
Regular Pyramida slant height of � units, and its base has a perimeter of P units and an area of B square units, then T � �
12
�P� � B.
For the regular square pyramid above, find the surface area to thenearest tenth if each side of the base is 12 centimeters and the height of thepyramid is 8 centimeters.Look at the pyramid above. The slant height is the hypotenuse of a right triangle. One leg ofthat triangle is the height of the pyramid, and the other leg is half the length of a side of thebase. Use the Pythagorean Theorem to find the slant height �.
�2 � 62 � 82 Pythagorean Theorem
� 100 Simplify.
� � 10 Take the square root of each side.
T � �12�P� � B Surface area of a pyramid
� �12�(4)(12)(10) � 122 P � (4)(12), � � 10, B � 122
� 384 Simplify.
The surface area is 384 square centimeters.
Find the surface area of each regular pyramid. Round to the nearest tenth ifnecessary.
1. 2.
3. 4.
5. 6.12 yd
10 yd
12 cm 13 cm
6 in.8.7 in. 15 in.
60�
10 cm
45�
8 ft
15 cm
20 cm
lateral edge
baseslant height height
Study Guide and Intervention (continued)
Surface Areas of Pyramids
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
ExampleExample
ExercisesExercises
Skills PracticeSurface Area of Pyramids
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 687 Glencoe Geometry
Less
on
12-
5
Find the surface area of each regular pyramid. Round to the nearest tenth ifnecessary.
1. 2.
3. 4.
5. 6.
7. 8.
16 in.
20 in.
18 m
12 m
6 yd
7 yd
9 mm
6 mm
14 ft
12 ft9 m
10 m
20 in.
8 in.4 cm
7 cm
© Glencoe/McGraw-Hill 688 Glencoe Geometry
Find the surface area of each regular pyramid. Round to the nearest tenth ifnecessary.
1. 2.
3. 4.
5. 6.
7. 8.
9. GAZEBOS The roof of a gazebo is a regular octagonal pyramid. If the base of thepyramid has sides of 0.5 meters and the slant height of the roof is 1.9 meters, find thearea of the roof.
4.5 m
12 m
5.2 yd
3 yd
15 mm
12 mm12 in.11 in.
8 cm
2.5 cm
13 ft
5 ft
12 m
7 m9 yd
10 yd
Practice Surface Area of Pyramids
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
Reading to Learn MathematicsSurface Areas of Pyramids
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 689 Glencoe Geometry
Less
on
12-
5
Pre-Activity How are pyramids used in architecture?
Read the introduction to Lesson 12-5 at the top of page 660 in your textbook.
Why do you think that the architect for the new entrance to the Louvredecided to use a pyramid rather than a rectangular prism?
Reading the Lesson
1. In the figure, ABCDE has congruent sides and congruent angles.
a. Describe this pyramid with as specific a name as possible.
b. Use the figure to name the base of this pyramid.
c. Describe the base of the pyramid.
d. Name the vertex of the pyramid.
e. Name the lateral faces of the pyramid.
f. Describe the lateral faces.
g. Name the lateral edges of the pyramid.
h. Name the altitude of the pyramid.
i. Write an expression for the height of the pyramid.
j. Write an expression for the slant height of the pyramid.
2. In a regular square pyramid, let s represent the side length of the base, h represent theheight, a represent the apothem, and � represent the slant height. Also, let L representthe lateral area and let T represent the surface area. Which of the followingrelationships are correct?
A. s � 2a B. a2 � �2 � h2 C. L � 4�s
D. h � ��2 � a�2� E. ��2s
��2 � h2 � �2 F. T � s2 � 2�s
Helping You Remember
3. A good way to remember something is to explain it to someone else. Suppose that one ofyour classmates is having trouble remembering the difference between the height andthe slant height of a regular pyramid. How can you explain this concept?
E D
CAS
B
Q
P
© Glencoe/McGraw-Hill 690 Glencoe Geometry
Two Truncated SolidsTo create a truncated solid, you could start with an ordinary solid and then cut off thecorners. Another way to make such a shape is to use the patterns on this page.
The Truncated Octahedron
1. Two copies of the pattern at the right can be used to make a truncated octahedron, a solid with 6 square faces and 8 regular hexagonal faces.
Each pattern makes half of the truncatedoctahedron. Attach adjacent faces using glue or tape to make a cup-shaped figure.
The Truncated Tetrahedron
2. The pattern below will make a truncated tetrahedron,a solid with 8 polygonal faces: 4 hexagons and 4 equilateral triangles.
Solve.
3. Find the surface area of the truncated octahedron if each polygon in the pattern has sides of 3 inches.
4. Find the surface area of the truncated tetrahedron if each polygon in the pattern has sides of 3 inches.
Area Formulas for Regular Polygons(s is the length of one side)
triangle A � �s42��3�
hexagon A � �32s2��3�
octagon A � 2s2(�2� � 1)
Tape orglue here.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
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Study Guide and InterventionSurface Areas of Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 691 Glencoe Geometry
Less
on
12-
6Lateral Areas of Cones Cones have the following properties.• A cone has one circular base and one vertex.• The segment whose endpoints are the vertex and
the center of the base is the axis of the cone.• The segment that has one endpoint at the vertex, is
perpendicular to the base, and has its other endpoint on the base is the altitude of the cone.
• For a right cone the axis is also the altitude, and any segment from the circumference of the base to the vertex is the slant height �. If a cone is not a right cone, it is oblique.
Lateral Area If a cone has a lateral area of L square units, a slant height of � units, of a Cone and the radius of the base is r units, then L � �r�.
Find the lateral area of a cone with slant height of 10 centimeters and a base with a radius of 6 centimeters.L � �r� Lateral area of a cone
� �(6)(10) r � 6, � � 10
� 188.5 Simplify.
The lateral area is about 188.5 square centimeters.
Find lateral area of each circular cone. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
8 yd
16 yd12 in.
5 in.
26 mm
20 mm
6��3 m
60�
9 cm
15 cm
3 cm4 cm
6 cm10 cm
axis
base base� slant height
right coneoblique cone
altitudeV V
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 692 Glencoe Geometry
Surface Areas of Cones The surface area of a cone is the lateral area of the cone plus the area of the base.
Surface Area If a cone has a surface area of T square units, a slant height of of a Right Cone � units, and the radius of the base is r units, then T � �r� � �r 2.
For the cone above, find the surface area to the nearest tenth if theradius is 6 centimeters and the height is 8 centimeters.The slant height is the hypotenuse of a right triangle with legs of length 6 and 8. Use thePythagorean Theorem.
�2 � 62 � 82 Pythagorean Theorem
�2 � 100 Simplify.
� � 10 Take the square root of each side.
T � �r� � �r2 Surface area of a cone
� �(6)(10) � � � 62 r � 6, � � 10
� 301.6 Simplify.
The surface area is about 301.6 square centimeters.
Find the surface area of each cone. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
60�
8��3 yd26 m
40 m
4 in.
45�12 cm
13 cm
5 ft
30�9 cm
12 cm
�slant height
height
r
Study Guide and Intervention (continued)
Surface Areas of Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
ExercisesExercises
ExampleExample
Skills PracticeSurface Areas of Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 693 Glencoe Geometry
Less
on
12-
6Find the surface area of each cone. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. Find the surface area of a cone if the height is 12 inches and the slant height is 15 inches.
8. Find the surface area of a cone if the height is 9 centimeters and the slant height is 12 centimeters.
9. Find the surface area of a cone if the height is 10 meters and the slant height is 14 meters.
10. Find the surface area of a cone if the height is 5 feet and the slant height is 7 feet.
4 yd6 yd
7 cm
22 cm
17 mm
9 mm
8 in.
21 in.
10 ft
25 ft14 m
5 m
© Glencoe/McGraw-Hill 694 Glencoe Geometry
Find the surface area of each cone. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. Find the surface area of a cone if the height is 8 feet and the slant height is 10 feet.
8. Find the surface area of a cone if the height is 14 centimeters and the slant height is16.4 centimeters.
9. Find the surface area of a cone if the height is 12 inches and the diameter is 27 inches.
10. HATS Cuong bought a conical hat on a recent trip to central Vietnam. The basic frame ofthe hat is 16 hoops of bamboo that gradually diminish in size. The hat is covered in palmleaves. If the hat has a diameter of 50 centimeters and a slant height of 32 centimeters,what is the lateral area of the conical hat?
7 cm21 cm5 m
4 m
3 ft 19 ft
48 yd
25 yd
7 mm18 mm
9 in.13 in.
Practice Surface Areas of Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
Reading to Learn MathematicsSurface Areas of Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 695 Glencoe Geometry
Less
on
12-
6Pre-Activity How is the lateral area of a cone used to cover tepees?
Read the introduction to Lesson 12-6 at the top of page 666 in your textbook.
If you wanted to build a tepee of a certain size, how would it help you toknow the formula for the lateral area of a cone?
Reading the Lesson
1.
a. Which net will give the cone with the greatest lateral area?
b. Which net will give the tallest cone?
2. Refer to the figure at the right. Suppose you have removed the circular base of the cone and cut from V to A so that you can unroll the lateralsurface onto a flat table.
a. How can you be sure that the flattened-out piece is a sector of a circle?
b. How do you know that the flattened-out piece is not a full circle?
3. Suppose you have a right cone with radius r, diameter d, height h, and slant height �.Which of the following relationships involving these lengths are correct?
A. r � 2d B. r � h � � C. r2 � h2 � �2
D. r2 � �2 � h2 E. r � ��2 � h�2� F. h � ���2 � r�2�
Helping You Remember
4. One way to remember a new formula is to relate it to a formula you already know.Explain how the formulas for the lateral areas of a pyramid and a cone are similar.
V
P A B
h
r
�
Net A Net B Net C
© Glencoe/McGraw-Hill 696 Glencoe Geometry
Cone Patterns
The pattern at the right is made from a circle. It can be folded to make a cone.
1. Measure the radius of the circle to the nearest centimeter.
2. The pattern is what fraction of the complete circle?
3. What is the circumference of the complete circle?
4. How long is the circular arc that is the outside of the pattern?
5. Cut out the pattern and tape it together to form a cone.
6. Measure the diameter of the circular base of the cone.
7. What is the circumference of the base of the cone?
8. What is the slant height of the cone?
9. Use the Pythagorean Theorem to calculate the height of the cone.Use a decimal approximation. Check your calculation by measuring the height with a metric ruler.
10. Find the lateral area.
11. Find the total surface area.
Make a paper pattern for each cone with the given measurements.Then cut the pattern out and make the cone. Find the measurements.
12. 13.
diameter of base � diameter of base �
lateral area � lateral area �
height of cone � height of cone �(to nearest tenth of a centimeter) (to nearest tenth of a centimeter)
20 cm120�6 cm
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
Study Guide and InterventionSurface Areas of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 697 Glencoe Geometry
Less
on
12-
7
Properties of Spheres A sphere is the locus of all points that are a given distance from a given point called its center.
Here are some terms associated with a sphere.• A radius is a segment whose endpoints are the
center of the sphere and a point on the sphere.• A chord is a segment whose endpoints are points
on the sphere.• A diameter is a chord that contains the sphere’s
center.• A tangent is a line that intersects the sphere in
exactly one point.• A great circle is the intersection of a sphere and
a plane that contains the center of the sphere.• A hemisphere is one-half of a sphere. Each great
circle of a sphere determines two hemispheres.
Determine the shapes you get when you intersect a plane with a sphere.
The intersection of plane M The intersection of plane N The intersection of plane Pand sphere O is point P. and sphere O is circle Q. and sphere O is circle O.
A plane can intersect a sphere in a point, in a circle, or in a great circle.
Describe each object as a model of a circle, a sphere, a hemisphere, or none of these.
1. a baseball 2. a pancake 3. the Earth
4. a kettle grill cover 5. a basketball rim 6. cola can
Determine whether each statement is true or false.
7. All lines intersecting a sphere are tangent to the sphere.
8. Every plane that intersects a sphere makes a great circle.
9. The eastern hemisphere of Earth is congruent to the western hemisphere.
10. The diameter of a sphere is congruent to the diameter of a great circle.
OPO
QN
O
PM
R�S� is a radius. A�B� is a chord.S�T� is a diameter. VX��� is a tangent.The circle that contains points S, M, T, and N isa great circle; it determines two hemispheres.
chord tangent
great circle
diameter
radius
S
T
W
RN
B
V
X
A
M
sphere
center
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 698 Glencoe Geometry
Surface Areas of Spheres You can think of the surface area of a sphere as the total area of all of the nonoverlapping strips it would take to cover thesphere. If r is the radius of the sphere, then the area of a great circle of thesphere is �r2. The total surface area of the sphere is four times the area of agreat circle.
Surface Area of a Sphere
If a sphere has a surface area of T square units and a radius of r units, then T � 4�r 2.
Find the surface area of a sphere to the nearest tenth if the radius of the sphere is 6 centimeters.T � 4�r2 Surface area of a sphere
� 4� � 62 r � 6
� 452.4 Simplify.
The surface area is 452.4 square centimeters.
Find the surface area of each sphere with the given radius or diameter to thenearest tenth.
1. r � 8 cm 2. r � 2�2� ft
3. r � � cm 4. d � 10 in.
5. d � 6� m 6. d � 16 yd
7. Find the surface area of a hemisphere with radius 12 centimeters.
8. Find the surface area of a hemisphere with diameter � centimeters.
9. Find the radius of a sphere if the surface area of a hemisphere is 192� square centimeters.
6 cm
r
Study Guide and Intervention (continued)
Surface Areas of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
ExercisesExercises
ExampleExample
Skills PracticeSurface Areas of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 699 Glencoe Geometry
Less
on
12-
7
In the figure, A is the center of the sphere, and plane Tintersects the sphere in circle E. Round to the nearesttenth if necessary.
1. If AE � 5 and DE � 12, find AD.
2. If AE � 7 and DE � 15, find AD.
3. If the radius of the sphere is 18 units and the radius of �E is 17 units, find AE.
4. If the radius of the sphere is 10 units and the radius of �E is 9 units, find AE.
5. If M is a point on �E and AD � 23, find AM.
Find the surface area of each sphere or hemisphere. Round to the nearest tenth.
6. 7.
8. a hemisphere with a radius of the great circle 8 yards
9. a hemisphere with a radius of the great circle 2.5 millimeters
10. a sphere with the area of a great circle 28.6 inches
32 m7 in.
A
ED
T
© Glencoe/McGraw-Hill 700 Glencoe Geometry
In the figure, C is the center of the sphere, and plane Bintersects the sphere in circle R. Round to the nearesttenth if necessary.
1. If CR � 4 and SR � 14, find CS.
2. If CR � 7 and SR � 24, find CS.
3. If the radius of the sphere is 28 units and the radius of �R is 26 units, find CR.
4. If J is a point on �R and CS � 7.3, find CJ.
Find the surface area of each sphere or hemisphere. Round to the nearest tenth.
5. 6.
7. a sphere with the area of a great circle 29.8 meters
8. a hemisphere with a radius of the great circle 8.4 inches
9. a hemisphere with the circumference of a great circle 18 millimeters
10. SPORTS A standard size 5 soccer ball for ages 13 and older has a circumference of27–28 inches. Suppose Breck is on a team that plays with a 28-inch soccer ball. Find thesurface area of the ball.
89 ft6.5 cm
C
RS
B
Practice Surface Areas of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
Reading to Learn MathematicsSurface Areas of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 701 Glencoe Geometry
Less
on
12-
7
Pre-Activity How do manufacturers of sports equipment use the surface areas of spheres?
Read the introduction to Lesson 12-7 at the top of page 671 in your textbook.
How would knowing the formula for the surface area of a sphere helpmanufacturers of beach balls?
Reading the Lesson1. In the figure, P is the center of the sphere. Name each of
the following in the figure.
a. three radii of the sphere
b. a diameter of the sphere
c. two chords of the sphere
d. a great circle of the sphere
e. a tangent to the sphere
f. the point of tangency
2. Determine whether each sentence is sometimes, always, or never true.
a. If a sphere and a plane intersect in more than one point, their intersection will be agreat circle.
b. A great circle has the same center as the sphere.c. The endpoints of a radius of a sphere are two points on the sphere.d. A chord of a sphere is a diameter of the sphere.e. A radius of a great circle is also a radius of the sphere.
3. Match each surface area formula with the name of the appropriate solid.
a. T � �r� � �r2 i. regular pyramid
b. T � Ph � 2B ii. hemisphere
c. T � 4�r2 iii. cylinder
d. T � �12�P� � B iv. prism
e. T � 2�rh � 2�r2 v. sphere
f. T � 3�r2 vi. cone
Helping You Remember4. Many students have trouble remembering all of the formulas they have learned in this
chapter. What is an easy way to remember the formula for the surface area of a sphere?
R S
T
P
W
V
X Y
U
© Glencoe/McGraw-Hill 702 Glencoe Geometry
Doubling SizesConsider what happens to surface area when the sides of a figure are doubled.
The sides of the large cube are twice the size of the sides of the small cube.
1. How long are the edges of the large cube?
2. What is the surface area of the small cube?
3. What is the surface area of the large cube?
4. The surface area of the large cube is how many times greater than that of the small cube?
The radius of the large sphere at the right is twice the radius of the small sphere.
5. What is the surface area of the small sphere?
6. What is the surface area of the large sphere?
7. The surface area of the large sphere is how many times greater than the surface area of the small sphere?
8. It appears that if the dimensions of a solid are doubled, the surface area is multiplied by ���������.
Now consider how doubling the dimensions affects the volume of a cube.
The sides of the large cube are twice the size of the small cube.
9. How long are the edges of the large cube?
10. What is the volume of the small cube?
11. What is the volume of the large cube?
12. The volume of the large cube is how many times greater than that of the small cube?
The large sphere at the right has twice the radius of the small sphere.
13. What is the volume of the small sphere?
14. What is the volume of the large sphere?
15. The volume of the large sphere is how many times greater than the volume of the small sphere?
16. It appears that if the dimensions of a solid are doubled, the volume is multiplied by ���������.
3 m
5 in.
3 m
5 in.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
Chapter 12 Test, Form 11212
© Glencoe/McGraw-Hill 703 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of eachquestion.
1. Which of these is part of an orthogonal drawing?A. a perspective view B. a corner viewC. a two-dimensional top view D. a three-dimensional view
For Questions 2–4, use the figure.
2. Identify this solid figure.A. square pyramid B. square prismC. triangular pyramid D. triangular prism
3. Name the base.A. �ABE B. �ABCD C. �CDE D. E
4. How many edges does this figure have?A. 3 B. 4 C. 6 D. 8
5. This net could be folded into a .A. tetrahedronB. square pyramidC. square prismD. triangular prism
6. Find the surface area of this solid.A. 9 in2 B. 27 in2
C. 36 in2 D. 54 in2
7. The areas of how many faces of a rectangular prism would be included in thelateral area?A. 2 B. 4 C. 6 D. 8
8. Find the surface area of a rectangular prism with a length of 8 inches, awidth of 5 inches, and a height of 2 inches.A. 15 in2 B. 66 in2 C. 80 in2 D. 132 in2
9. The area of each face of a cube is 60 square centimeters. Find the surfacearea of the cube.A. 120 cm2 B. 240 cm2 C. 360 cm2 D. 3600 cm2
10. The lateral area of a right cylinder with a radius of 10 feet is 320� squarefeet. Find the surface area of the cylinder.A. 220� ft2 B. 360� ft2 C. 420� ft2 D. 520� ft2
3 in.3 in.
3 in.
6 in.
4 in.4 in. 4 in.
4 in.
4 in.
?
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 704 Glencoe Geometry
Chapter 12 Test, Form 1 (continued)1212
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use the figure.
11. Find the lateral area to the nearest tenth.A. 75.4 ft2 B. 62.8 ft2
C. 50.3 ft2 D. 25.1 ft2
12. Find the surface area to the nearest tenth.A. 75.4 ft2 B. 62.8 ft2 C. 50.3 ft2 D. 25.1 ft2
13. The lateral area of a regular pyramid is 300 square units. The perimeter of itsbase is 100 units. Find the slant height of the pyramid.A. 3 units B. 6 units C. 12 units D. 30 units
For Questions 14 and 15, use the figure.
14. Find the lateral area.A. 108 cm2 B. 144 cm2
C. 162 cm2 D. 324 cm2
15. Find the surface area.A. 108 cm2 B. 144 cm2 C. 162 cm2 D. 324 cm2
16. Find the surface area to the nearest tenth.A. 546.6 units2 B. 989.6 units2
C. 1017.9 units2 D. 1046.2 units2
17. The radius of a right circular cone is 6 inches and the height is 8 inches. Findthe slant height.A. 2 in. B. 4 in. C. 10 in. D. 14 in.
18. A cone has a radius 17 inches long and slant height 20 inches long. Find thesurface area to the nearest tenth.A. 18,158.4 in2 B. 1976.1 in2 C. 1068.1 in2 D. 340 in2
19. Which could be the intersection of a sphere and a plane?A. line B. square C. oval D. point
20. A sphere has a diameter 42 centimeters long. Find the surface area to thenearest tenth.A. 5541.8 cm2 B. 2770.9 cm2 C. 2167.1 cm2 D. 527.8 cm2
Bonus Find the amount of glass needed to cover the sides of thegreenhouse shown. The bottom,front, and back are not glass.
15 ft
30 ft
9 ft
9 ft
8 ft8 ft
50
5
6
6 cm6 cm
9 cm
2 ft
4 ft
B:
NAME DATE PERIOD
Chapter 12 Test, Form 2A1212
© Glencoe/McGraw-Hill 705 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of eachquestion.
1. What do the dark segments represent in an orthogonal drawing?A. a change in color B. where paper should be foldedC. a design on the surface D. a break in the surface
For Questions 2 and 3, use the figure.2. Identify the figure.
A. pyramid B. prismC. cone D. cylinder
3. Name the base.A. X B. Y C. X�Y� D. �Y
4. What name is given to a prism having five faces?A. pentagonal prism B. square prismC. triangular prism D. none of these
5. This net could be folded into a .A. cone B. cylinderC. sphere D. triangular prism
6. Find the surface area of the solid.A. 188 ft2 B. 240 ft2
C. 288 ft2 D. 480 ft2
7. The lateral area of a cube is 36 square inches. How long is each edge?A. �6� in. B. 3 in. C. 6 in. D. 9 in.
8. The lateral area of a prism is 56 square inches and the area of each base is 17 square inches. Find the surface area of the prism.A. 952 in2 B. 90 in2 C. 73 in2 D. 22 in2
9. Find the surface area of the outside of the open box.A. 1920 in2 B. 998 in2
C. 752 in2 D. 400 in2
10. The surface area of a right cylinder is 200� square centimeters and theradius is 4 centimeters. Find the height.A. 42 cm B. 25 cm C. 23 cm D. 21 cm
20 in.12 in.
8 in.
10 ft8 ft
6 ft
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 706 Glencoe Geometry
Chapter 12 Test, Form 2A (continued)1212
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use a right cylinder with a radius of 3 inchesand a height of 17 inches. Round to the nearest tenth.
11. Find the lateral area.A. 320.4 in2 B. 348.7 in2 C. 377.0 in2 D. 537.2 in2
12. Find the surface area.A. 320.4 in2 B. 348.7 in2 C. 377.0 in2 D. 537.2 in2
13. The lateral area of a regular pentagonal pyramid is 75 square inches and theslant height is 10 inches. Find the length of each side of the base.A. 15 in. B. 14 in. C. 7.5 in. D. 3 in.
For Questions 14 and 15, use the figure.
14. Find the lateral area.A. 144 cm2 B. 144 � 24�3� cm2
C. 196 cm2 D. 288 cm2
15. Find the surface area.A. 144 cm2 B. 144 � 24�3� cm2 C. 196 cm2 D. 288 cm2
For Questions 16 and 17, use the figure.Round to the nearest tenth.
16. Find the lateral area.A. 44.0 in2 B. 75.4 in2 C. 88.0 in2 D. 100.5 in2
17. Find the surface area.A. 44.0 in2 B. 75.4 in2 C. 88.0 in2 D. 100.5 in2
18. Find the surface area of this model rocket to the nearest tenth.A. 2890.3 cm2 B. 2576.1 cm2
C. 2513.3 cm2 D. 2261.9 cm2
For Questions 19 and 20, use the figure.
19. Identify a chord.A. E�F� B. �B C. B�D� D. AD�
20. Find the surface area to the nearest tenth.A. 4536.5 m2 B. 2268.2 m2 C. 477.5 m2 D. 238.8 m2
Bonus Find the surface area of the figure to the nearest tenth.
4 ft
12 ft
1 ft
19 mA C
D
E F
B
10 cm
30 cm
12 cm
12 in.2 in.
12 in.
4 in.
B:
NAME DATE PERIOD
Chapter 12 Test, Form 2B1212
© Glencoe/McGraw-Hill 707 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of eachquestion.
1. Given the corner view of a figure, which is the top view?A. B. C. D.
For Questions 2 and 3, use the figure.
2. Identify the figure.A. pyramid B. prismC. cone D. cylinder
3. Name a base.A. �M B. N C. M�N� D. M
4. What name is given to a pyramid having seven faces?A. heptagonal pyramid B. hexagonal pyramidC. pentagonal pyramid D. octagonal pyramid
5. This net could be folded into a .A. rectangular pyramidB. rectangular prismC. triangular pyramidD. triangular prism
6. Find the surface area of the solid.A. 88 cm2 B. 102 cm2
C. 156 cm2 D. 160 cm2
7. Find the lateral area of an equilateral triangular prism if the area of eachlateral face is 10 square centimeters.A. 10�3� cm2 B. 30 cm2 C. 50 cm2 D. 100 cm2
8. The surface area of a cube is 96 square inches. Find the length of an edge.A. �24� in. B. 4 in. C. 8 in. D. 16 in.
9. The surface area of a rectangular prism is 190 square inches, the length is 10 inches, and the width 3 inches. Find the height.A. 30 in. B. 20 in. C. 10 in. D. 5 in.
10. A right cylinder has a radius of 2 feet and a height of 5 feet. Find its surfacearea.A. 20� ft2 B. 28� ft2 C. 36� ft2 D. 40� ft2
4 cm
5 cm
2 cm
8 cm
4 in.
8 in.
8 in.8 in.
5 in.
4 in.
5 in. 5 in.
?
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© Glencoe/McGraw-Hill 708 Glencoe Geometry
Chapter 12 Test, Form 2B (continued)1212
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use a right cylinder with a radius of 5 centimeters and a height of 22 centimeters. Round to the nearest tenth.
11. Find the lateral area.A. 848.2 cm2 B. 769.7 cm2 C. 691.2 cm2 D. 345.6 cm2
12. Find the surface area.A. 848.2 cm2 B. 769.7 cm2 C. 691.2 cm2 D. 345.6 cm2
13. Find the lateral area of the conical hat to the nearest tenth.A. 942.5 in2 B. 408.4 in2
C. 204.2 in2 D. 188.5 in2
For Questions 14 and 15, use a tetrahedron that has edges of length 12 centimeters.14. Find the lateral area.
A. 48�3� cm2 B. 96�3� cm2 C. 108�3� cm2 D. 144�3� cm2
15. Find the surface area.A. 48�3� cm2 B. 96�3� cm2 C. 108�3� cm2 D. 144�3� cm2
For Questions 16 and 17, use the figure. Round to the nearest tenth.16. Find the lateral area.
A. 75.4 cm2 B. 103.7 cm2
C. 131.9 cm2 D. 150.8 cm2
17. Find the surface area.A. 75.4 cm2 B. 103.7 cm2 C. 131.9 cm2 D. 150.8 cm2
18. Find the surface area of the solid to the nearest tenth.A. 62.8 cm2 B. 56.5 cm2
C. 47.1 cm2 D. 37.7 cm2
19. Name a tangent to the sphere.A. Y�U� B. X�Z�C. UZ� D. WV���
20. The surface area of a sphere is 64� square centimeters. Find the radius.A. 16 cm B. 8 cm C. 4 cm D. 2 cm
Bonus Find the surface area of the frustum of a square pyramid.
3 ft
2 ft
4 ft
X Z
U
VW
Y
1 cm
6 cm
3 cm3 cm
3 cm8 cm
12 in.
5 in.
B:
NAME DATE PERIOD
Chapter 12 Test, Form 2C1212
© Glencoe/McGraw-Hill 709 Glencoe Geometry
Ass
essm
ents
1. Given the corner view of a figure,sketch the front view.
2. Name the faces of the solid.
3. Identify the solid.
4. How many faces does a dodecahedron have?
5. Draw a net for the solid.
6. Find the surface area of the solid.
7. Find the lateral area of a triangular prism with a height of 8 centimeters, and with bases having sides that measure 4 centimeters, 5 centimeters, and 6 centimeters.
8. Find the surface area of the prism.
9. Find the surface area of the solid to the nearest tenth.
10. A gallon of paint costs $12.99 and covers 400 square feet. Howmany gallons are needed to paint two coats on the walls andceiling (not the floor) of a rectangular room that is 30 feet long,18 feet wide, and 8 feet high? Round to the next whole gallon.
1 in.
1 in.
1 in.
0.25 in.
25
25
5014
12 in.6 in.
5 in.
65
4
P S
RQ
T
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NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 710 Glencoe Geometry
Chapter 12 Test, Form 2C (continued)1212
11. Find the lateral area of a right cylinder with a diameter of 8.6 yards and a height of 19.4 yards. Round to the nearest tenth.
12. The surface area of a cylinder is 180� square inches and theheight is 9 inches. Find the radius.
For Questions 13 and 14, use a regular hexagonal pyramidwith base edges of 10 inches and a slant height of 9 inches.
13. Find the lateral area.
14. Find the surface area.
15. Find the lateral area of the triangular pyramid.
16. The surface area of a regular pyramid is 276 square centimeters,the slant height measures 8 centimeters, and the area of thebase is 50 square centimeters. Find the perimeter of the base.
For Questions 17 and 18, use a right circular cone with aradius of 4 feet and a height of 3 feet. Round to the nearesttenth.
17. Find the lateral area.
18. Find the surface area.
19. Plane A intersects sphere R in �X.Find the radius of the sphere.
20. Find the surface area of this hemisphere to the nearest tenth.
Bonus The surface area of the exterior of a hollow rubber ball is
16� square inches. The rubber is �14� inch thick. Find the
surface area of the interior of the ball.
5 cm
R
XA
15 m 8 m
101010
12
12
12
NAME DATE PERIOD
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B:
Chapter 12 Test, Form 2D1212
© Glencoe/McGraw-Hill 711 Glencoe Geometry
Ass
essm
ents
1. Given the corner view of a figure,sketch the back view.
2. Name the edges of the solid.
3. Identify the solid.
4. How many edges does a cube have?
5. Draw a net for the solid.
6. Find the surface area of the solid.
7. Find the lateral area of a regular pentagonal prism if theperimeter of the base is 50 inches and the height is 15 inches.
8. Find the surface area of the prism.
9. A gallon of paint costs $18 and covers 300 square feet. Howmany gallons are needed to paint the walls and bottom of arectangular swimming pool whose length is 25 feet, width is16 feet, and depth is 4 feet? Round to the next whole gallon.
10. Find the surface area of the solid.
6 in.6 in.
4 in.
4 in.
9 ft5 ft
6 ft
17 cm
17 cm16 cm
12 cm
88
8
6
6
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I
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66
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 712 Glencoe Geometry
Chapter 12 Test, Form 2D (continued)1212
11. A right cylinder has a diameter of 23.6 meters and a height of11.4 meters. Find the lateral area to the nearest tenth.
12. The surface area of a right cylinder is 252� square feet andthe height is 11 feet. Find the radius.
For Questions 13 and 14, use a regular octagonal pyramidwith base edges 9 feet long, slant height 15 feet, and a basewith an apothem of 10.86 feet.
13. Find the lateral area.
14. Find the surface area to the nearest tenth.
15. Find the lateral area of the solid to the nearest tenth.
16. The surface area of a regular decagonal pyramid is 1800 squarefeet, the area of the base is 120 square feet, and the slantheight is 15 feet. Find the length of each side of the base.
For Questions 17 and 18, use a cone with a radius of 5 centimeters and a height of 12 centimeters. Round to thenearest tenth.
17. Find the lateral area.
18. Find the surface area.
19. Plane A intersects sphere B in �C.Find BC.
20. Find the surface area of this hemisphere to the nearest tenth.
Bonus The length of each side of a cube is 6 inches long. Find thesurface area of a sphere inscribed in the cube.
11 in.
B
CA
13 m12 m
1818
10
NAME DATE PERIOD
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B:
Chapter 12 Test, Form 31212
© Glencoe/McGraw-Hill 713 Glencoe Geometry
Ass
essm
ents
1. Draw the back view of a figure given its orthogonaldrawing.
2. Name the bases of the solid.
3. Identify the solid.
4. How many faces does an icosahedron have?
5. Draw a net for the solid.
6. Find the surface area of the solid.
7. Find the lateral area of a triangular prism with a righttriangular base with legs that measure 2 feet and 3 feet and a height of 7 feet.
8. Find the surface area of the prism.
For Questions 9 and 10, use a right cylinder with adiameter of 96.4 feet and a height of 58.9 feet. Round to thenearest tenth.
9. Find the lateral area.
10. Find the surface area.
11. If the height of a right cylinder is multiplied by four and theradius remains the same, what happens to the lateral area?
6
10
20
84
3
��21
3
2
2
2
5
XZ
YV
U
W
top view left view front view right view
1.
2.
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22
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NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 714 Glencoe Geometry
Chapter 12 Test, Form 3 (continued)1212
For Questions 12 and 13, use the solid.
12. Find the lateral area.
13. Find the surface area to the nearest tenth.
14. If the length of each side of a cube is tripled, what happens tothe surface area?
For Questions 15 and 16, use a right circular cone with aradius of 7 inches and a height of 8 inches. Round to thenearest tenth.
15. Find the lateral area.
16. Find the surface area.
17. Find the surface area of this frustum of a cone, to the nearest tenth.
18. Parallel planes A and B intersect sphere C in circles D and E and DC � 6. Find CE.
19. Write a formula for the surface area of a hemisphere in termsof � and the radius r.
20. Find the surface area of the solid to the nearest square foot.
Bonus Find the surface area of the solid to the nearest square foot. Do notinclude the area of the base.
8 ft
10 ft
6 ft
8 ft 22 ft
B
E
C
D8
4
A
B
D
6 cm
4 cm
2 cm
13 in.
12 in.
NAME DATE PERIOD
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B:
Chapter 12 Open-Ended Assessment1212
© Glencoe/McGraw-Hill 715 Glencoe Geometry
Ass
essm
ents
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.
1. a. Complete this chart.
b. Write a formula relating the number of edges to the number of facesand vertices.
2. Explain the difference between the lateral area and the surface area of a prism.
3. a. Draw and label a pyramid.
b. Name the base.
c. Name the lateral faces.
d. Draw a net for your pyramid.
4. Draw an oblique cylinder and a right cylinder.
5. a. Draw and label the dimensions of a solid figure composed of three ormore different solids studied in this chapter.
b. Find the surface area.
6. Write a practical application problem involving the surface area or lateralarea of a solid figure studied in this chapter.
Figure No. of Edges (e) No. of Faces (f ) No. of Vertices (v ) f � v
Triangular Pyramid 6 4 4 8
Triangular Prism
Cube
Square Pyramid
Hexagonal Prism
Hexagonal Pyramid
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 716 Glencoe Geometry
Chapter 12 Vocabulary Test/Review1212
Choose from the terms above to complete each sentence.
1. The height of each lateral face of a regular pyramid is calleda(n) .
2. A(n) has a circular base and a vertex.
3. A(n) is a set of points in space that are a givendistance from a given point.
4. The view of a solid figure from the corner is called a cornerview or .
5. The five types of regular polyhedra are called the .
6. A(n) is a polyhedron with two parallel congruent facescalled bases.
7. A polyhedron that has all but one face intersecting at onepoint is a(n) .
8. The is the sum of the areas of all the faces of the solid.
9. If the axis of a cylinder is also the altitude, then the cylinderis called a(n) .
10. A sphere is separated by a great circle into two congruenthalves, each called a(n) .
Define each term.
11. lateral area
12. right prism
13. great circle
?
?
?
?
?
?
?
?
?
?1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
axisbasescircular coneconecorner viewcross sectioncylinderedgesface
great circlehemispherelateral arealateral edgeslateral facesnetoblique coneoblique cylinder
oblique prismorthogonal drawingperspective viewPlatonic solidspolyhedronprismpyramidregular polyhedron
regular prismregular pyramidright coneright cylinderright prismslant heightspheresurface area
NAME DATE PERIOD
SCORE
Chapter 12 Quiz (Lessons 12–1 and 12–2)
1212
© Glencoe/McGraw-Hill 717 Glencoe Geometry
Ass
essm
ents
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
1. Given the corner view of a figure,draw the left view.
2. Draw a rectangular prism.
3. Draw a net for this solid.
4. STANDARDIZED TEST PRACTICE Find the surface area of the solid formed by folding this net.A. 48 in2 B. 64 in2
C. 72 in2 D. 88 in2 2 in.
2 in.
2 in.
4 in.
4 in.
6 in.
210
1022
22
2
22 22
2
2222
2
Chapter 12 Quiz (Lessons 12–3 and 12–4)
1212
1.
2.
3.
4.
5.
1. The lateral area of a prism is 70 square inches and theperimeter of its base is 35 inches. Find the height.
2. The surface area of a rectangular prism is 592 square units.The height is 10 units and the width is 8 units. Find the length.
3. Describe the shape of a net that could be used to calculate thelateral area of a cylinder.
For Questions 4 and 5, use the solid figure. Round to the nearest tenth.
4. Find the lateral area.
5. Find the surface area.
11
56
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 718 Glencoe Geometry
Chapter 12 Quiz (Lessons 12–5 and 12–6)
1212
1.
2.
3.
4.
5.
For Questions 1 and 2, use the solid figure.
1. Find the lateral area.
2. Find the surface area to the nearest tenth.
3. The lateral area of a pyramid is 200 square centimeters and thebase is a rectangle with a length measuring 15 centimetersand a width measuring 4 centimeters. Find the surface area ofthe pyramid.
For Questions 4 and 5, use a right circular cone with aradius of 5 feet and a slant height of 12 feet. Round to thenearest tenth.
4. Find the lateral area.
5. Find the surface area.
6
9
9
9
NAME DATE PERIOD
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Chapter 12 Quiz (Lesson 12–7)
1212
1.
2.
3.
4.
5.
For Questions 1–3, use the figure.
1. Name a chord of sphere D that is not adiameter.
2. Name a tangent to the sphere.
3. Name a great circle.
4. A sphere has a radius that is 18 inches long. Find the surfacearea to the nearest tenth.
5. The radius of a sphere is doubled. How is the surface areachanged?
E
A
H
F
G
BC
D
NAME DATE PERIOD
SCORE
Chapter 12 Mid-Chapter Test (Lessons 12–1 through 12–3)
1212
© Glencoe/McGraw-Hill 719 Glencoe Geometry
Ass
essm
ents
1. Which of these are Platonic solids?A. cylinder, cone, sphere B. prism, pyramidC. tetrahedron, octahedron, dodecahedron D. hexagon, octagon, dodecagon
2. Which of the following describes a tetrahedron?A. triangular pyramid B. triangular prismC. square pyramid D. cone
3. The surface area of a prism is 120 square centimeters and the area of eachbase is 32 square centimeters. Find the lateral area of the prism.A. 184 cm2 B. 152 cm2 C. 86 cm2 D. 56 cm2
For Questions 4 and 5, use the solid figure. Round to the nearest tenth.4. Find the lateral area.
A. 9289.1 ft2 B. 9434.2 ft2
C. 10,965.4 ft2 D. 12,641.8 ft2
5. Find the surface area.A. 9289.1 ft2 B. 9434.2 ft2 C. 10,965.4 ft2 D. 12,641.8 ft2
46.2 ft
64 ft
6.
7.
8.
9.
10.
6
5
5
4
4
4 53
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
5.
Part II
6. Draw the top view of the solid figure.
7. Draw a net of the solid.
8. Find the surface area of the solid formed by folding this net.
9. Find the surface area of the regular hexagonal prism to the nearest tenth.
10. Find the total surface area to the nearest tenth. 4 in.
6 in.
1 in.
2 6
30
15
15
18
5
64
3
Part I Write the letter for the correct answer in the blank at the right of each question.
© Glencoe/McGraw-Hill 720 Glencoe Geometry
Chapter 12 Cumulative Review(Chapters 1–12)
1212
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
1. Name two obtuse vertical angles.(Lesson 1-5)
2. Use the statements p: �8 � 3 � 5 and q: A triangle has foursides to find the truth value of p � q. (Lesson 2-2)
3. Find the value of �1x�, where x initially equals 2. Then, use that
value as the next x in the expression. Repeat the process anddescribe your observations. (Lesson 6-6)
4. Find m�X and m�Z to the nearest degree and y to the nearest centimeter.(Lesson 7-7)
5. Each side of a rhombus is 18 inches long. One diagonal makesa 40° angle with one side. What is the length of each diagonalto the nearest tenth? (Lesson 8-5)
6. Find the magnitude and direction of ST� for S(4, �1) andT(�6, 5). Round to the nearest tenth. (Lesson 9-6)
7. A certain figure is the locus of all points in a plane equidistantfrom point B. What is the shape of this figure? (Lesson 10-1)
8. Find m�C. (Lesson 10-6)
9. Find the area and perimeter.(Lesson 11-1)
10. The surface area of a cube is 1261.5 square meters. Find thelength of a lateral edge of the cube. (Lesson 12-3)
11. The surface area of a right cylinder is 502.7 square inches andthe height is 11 inches. Find the radius of the base to thenearest tenth. (Lesson 12-4)
6 cm
4 cm
4 cm
7 cm
3 cm2 cm
88� 32�
E
A
D
BC
73�
32 cm
25 cmy
Z Y
X
18�
74�
EA D
BF
C
NAME DATE PERIOD
SCORE
Standardized Test Practice (Chapters 1–12)
© Glencoe/McGraw-Hill 721 Glencoe Geometry
1. Which method could you use to prove B�E� � A�C� if AF � BF? (Lesson 4-5)
A. Show that �ABE � �BAC by SSS,then B�E� � A�C� by CPCTC.
B. Show that �ABE � �BAC by ASA, then B�E� � A�C� by CPCTC.C. Show that �BFE � �AFC by SAS, then B�E� � A�C� by CPCTC.D. Show that �ABE � �BAC by AAS, then B�E� � A�C� by CPCTC.
2. Find a. (Lesson 6-3)
E. 28.5 F. 6.3G. 12.6 H. 14
3. Find r. (Lesson 7-6)
A. about 34.0 B. about 11.8C. about 8.9 D. about 6.6
4. A square has side length 18 centimeters. Find the area of thesquare. (Lesson 8-5)
E. 36 cm2 F. 40 cm2 G. 81 cm2 H. 324 cm2
5. What can you assume from the figure? (Lesson 10-3)
A. �ABC is isosceles.B. �ABC is equilateral.C. DF � EGD. radius of �O � x � y
6. Points D, E, and F are on a circle so that mDEF�� 210. Suppose
point G is randomly located on the same circle so that it does notcoincide with D, E, or F. What is the probability that m�DGF �105? (Lesson 10-4)
E. �172� F. �1
52� G. 1 H. �
34�
7. Which net could be folded into a triangular prism? (Lesson 12-2)
A. B. C. D.
8. Find the surface area of a square pyramid with a height of 9 centimeters and base with a side measuring 24 centimeters.(Lesson 12-5)
E. 1296 cm2 F. 1806 cm2 G. 2016 cm2 H. 8640 cm2
x
yxO
B
A F G
C
E
D
97�
49�
8.9
r
Q R
P
40�
40�
4.2
12.6
9.5
a
A
B E
C
F
NAME DATE PERIOD
SCORE 1212
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
1.
2.
3.
4.
5.
6.
7.
8. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
Ass
essm
ents
© Glencoe/McGraw-Hill 722 Glencoe Geometry
Standardized Test Practice (continued)
9. Quadrilateral PQSRis a rectangle.Find a. (Lesson 8-4)
10. Find x. Assume that segments that appeartangent are tangent.(Lesson 10-5)
2x � 8
5x � 7
M
N
(2a � 1)�(6a � 21)�
P Q
SR
NAME DATE PERIOD
1212
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
Part 3: Short Response
Instructions: Show your work or explain in words how you found your answer.
9. 10.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
11. Find the length of SR� to the nearest tenth. (Lesson 10-2)
12. Find x. (Lesson 10-7)
13. Find the area of the shaded region to the nearest tenth. (Lesson 11-3)
14. Identify the solid. (Lesson 12-1)
15. A right circular cone has a slant height of 15 inches and aradius that is 25 inches long. Find the surface area to thenearest tenth. (Lesson 12-6)
16. A ball has a diameter of 26.5 centimeters. Find the surfacearea of the ball to the nearest tenth. (Lesson 12.7)
10 cm
60� 60�
60�
15
3018
x
50�
3 mT
S
R
11.
12.
13.
14.
15.
16.
1 4 5
Standardized Test PracticeStudent Record Sheet (Use with pages 684–685 of the Student Edition.)
1212
© Glencoe/McGraw-Hill A1 Glencoe Geometry
An
swer
s
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9 DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
Part 1 Multiple ChoicePart 1 Multiple Choice
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Open-EndedPart 3 Open-Ended
Solve the problem and write your answer in the blank.
Also enter your answer by writing each number or symbol in a box. Then fill inthe corresponding oval for that number or symbol.
10 (grid in) 10 11 12
11 (grid in)
12 (grid in)0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
Record your answers for Questions 13–14 on the back of this paper.
© Glencoe/McGraw-Hill A2 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Th
ree-
Dim
ensi
on
al F
igu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill66
1G
lenc
oe G
eom
etry
Lesson 12-1
Dra
win
gs
of
Thre
e-D
imen
sio
nal
Fig
ure
sT
o w
ork
wit
h a
th
ree-
dim
ensi
onal
obje
ct,a
use
ful
skil
l is
th
e ab
ilit
y to
mak
e an
ort
hog
onal
dra
win
g,w
hic
h i
s a
set
of t
wo-
dim
ensi
onal
dra
win
gs o
f th
e di
ffer
ent
side
s of
th
e ob
ject
.For
a s
quar
e py
ram
id,y
ou w
ould
show
th
e to
p vi
ew,t
he
left
vie
w,t
he
fron
t vi
ew,a
nd
the
righ
t vi
ew.
Dra
w t
he
bac
k v
iew
of
the
figu
re
give
n t
he
orth
ogon
al d
raw
ing.
•T
he
top
view
in
dica
tes
two
colu
mn
s.•
Th
e le
ft v
iew
in
dica
tes
that
th
e h
eigh
t of
fig
ure
is
thre
e bl
ocks
.•
Th
e fr
ont
view
in
dica
tes
that
th
e co
lum
ns
hav
e h
eigh
ts 2
an
d 3
bloc
ks.
•T
he
righ
t vi
ew i
ndi
cate
s th
at t
he
hei
ght
of t
he
figu
re i
s th
ree
bloc
ks.
Use
blo
cks
to m
ake
a m
odel
of
the
obje
ct.T
hen
use
you
r m
odel
to
draw
th
e ba
ck v
iew
.Th
e ba
ck v
iew
in
dica
tes
that
th
e co
lum
ns
hav
e h
eigh
ts
3 an
d 2
bloc
ks.
Dra
w t
he
bac
k v
iew
an
d c
orn
er v
iew
of
a fi
gure
giv
en e
ach
ort
hog
onal
dra
win
g.
1.2.
3.4.
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wob
ject
top
view
left
view
front
vie
wrig
ht v
iew
obje
ctto
p vi
ewle
ft vi
ewfro
nt v
iew
right
vie
w
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill66
2G
lenc
oe G
eom
etry
Iden
tify
Th
ree-
Dim
ensi
on
al F
igu
res
A p
olyh
edro
nis
a s
olid
wit
h a
ll f
lat
surf
aces
.Eac
h s
urf
ace
of a
pol
yhed
ron
is
call
ed a
fac
e,an
d ea
ch l
ine
segm
ent
wh
ere
face
sin
ters
ect
is c
alle
d an
ed
ge.T
wo
spec
ial
kin
ds o
f po
lyh
edra
are
pri
sms,
for
wh
ich
tw
o fa
ces
are
con
gru
ent,
para
llel
bas
es,a
nd
pyr
amid
s,fo
r w
hic
h o
ne
face
is
a ba
se a
nd
all
the
oth
erfa
ces
mee
t at
a p
oin
t ca
lled
th
e ve
rtex
.Pri
sms
and
pyra
mid
s ar
e n
amed
for
th
e sh
ape
ofth
eir
base
s,an
d a
regu
lar
poly
hed
ron
has
a r
egu
lar
poly
gon
as
its
base
.
Oth
er s
olid
s ar
e a
cyli
nd
er,w
hic
h h
as c
ongr
uen
t ci
rcu
lar
base
s in
par
alle
l pl
anes
,a c
one,
wh
ich
has
on
e ci
rcu
lar
base
an
d a
vert
ex,a
nd
a sp
her
e.
Iden
tify
eac
h s
olid
.Nam
e th
e b
ases
,fac
es,e
dge
s,an
d v
erti
ces.
pent
agon
alpr
ism
squa
repy
ram
idpe
ntag
onal
pyra
mid
rect
angu
lar
pris
msp
here
cone
cylin
der
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Th
ree-
Dim
ensi
on
al F
igu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
Exam
ple
Exam
ple
a.
Th
e fi
gure
is
a re
ctan
gula
r py
ram
id.T
he
base
is
rect
angl
e A
BC
D,a
nd
the
fou
r fa
ces
�A
BE
,�B
CE
,�
CD
E,a
nd
�A
DE
mee
t at
ver
tex
E.T
he
edge
s ar
eA �
B�,B�
C�,C�
D�,A�
D�,A�
E�,B�
E�,C�
E�,a
nd
D�E�
.Th
e ve
rtic
esar
e A
,B,C
,D,a
nd
E.
E
AB
CD
b.
Th
is s
olid
is
a cy
lin
der.
Th
etw
o ba
ses
are
�O
and
�P
.
PO
Exer
cises
Exer
cises
Iden
tify
eac
h s
olid
.Nam
e th
e b
ases
,fac
es,e
dge
s,an
d v
erti
ces.
1.2.
3.4.
Th
e fa
ces
are
pen
tag
on
s P
WX
YZ
�D
EF
.Th
e fa
ces
are
�A
BC
and
an
d R
QV
US
and
par
alle
log
ram
s �
DE
Fan
d p
aral
lelo
gra
ms
AC
FD
,Z
SU
Y,X
YU
V,W
XV
Q,P
RQ
W,a
nd
A
BE
D,a
nd
BE
FC
.Th
e ed
ges
are
ZP
RS
.Th
e ed
ges
are
Z�S�
,Y�U�
,X�V�
,W�Q�
,A�
B�,B�
C�,A�
C�,C�
F�,A�
D�,B�
E�,D�
E�,E�
F�,P�
R�,Z�
Y�,Y�
X�,X�
W�,W�
P�,P�
Z�,S�
U�,U�
V�,V�
Q�,
and
D�F�.
Th
e ve
rtic
es a
re A
,B,C
,Q�
R�,a
nd
R�S�
.Th
e ve
rtic
es a
re P
,W,X
,D
,E,a
nd
F.
Y,Z
,R,Q
,V,U
,an
d S
.
Th
e so
lid is
atr
ian
gu
lar
pri
sm.
Th
e b
ases
are
�A
BC
and
AB
CF
DE
Th
e fi
gu
re is
ap
enta
go
nal
pri
sm.T
he
bas
es a
re p
enta
go
ns
PW
XY
Zan
d R
QV
US
.P
WQV
ZX
U
S R
Y
Th
e so
lid is
a s
ph
ere
wit
h c
ente
r T
.T
Th
e so
lid is
a c
on
e.It
has
�S
fo
r a
bas
ean
d v
erte
x R
.SR
Answers (Lesson 12-1)
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Th
ree-
Dim
ensi
on
al F
igu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill66
3G
lenc
oe G
eom
etry
Lesson 12-1
Dra
w t
he
bac
k v
iew
an
d c
orn
er v
iew
of
a fi
gure
giv
en e
ach
ort
hog
onal
dra
win
g.
1.2.
Iden
tify
eac
h s
olid
.Nam
e th
e b
ases
,fac
es,e
dge
s,an
d v
erti
ces.
3.
rect
ang
ula
r p
rism
;sa
mp
le a
nsw
er:
bas
es:
�R
ST
U,�
VW
XY
;fa
ces:
�R
ST
U,�
RS
XY
,�V
WX
Y,�
TU
VW
,�S
TW
X,�
RU
VY
;ed
ges
:R�
S�,R�
U�,S�
T�,T�U�
,S�X�
,R�Y�
,T�W�
,U�V�
,V�Y�
,W�X�
,X�Y�
,V�W�
;ve
rtic
es:
R,S
,T,U
,V,W
,X,a
nd
Y
4.
pen
tag
on
al p
yram
id;
bas
e:p
enta
go
n A
BC
DE
;fa
ces:
pen
tag
on
AB
CD
E,�
AF
B,�
BF
C,�
CF
D,�
DF
E,�
AF
E;
edg
es:
A�B�
,B�C�
,C�D�
,D�E�
,A�E�
,A�F�,
B�F�,
C�F�,
D�F�,
E�F�
;ve
rtic
es:
A,B
,C,D
,E,a
nd
F
5.
con
e;b
ase:
circ
le R
;ve
rtex
:S
SR
F
AB
CD
E
UT
WV
RS
XY
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
©G
lenc
oe/M
cGra
w-H
ill66
4G
lenc
oe G
eom
etry
Dra
w t
he
bac
k v
iew
an
d c
orn
er v
iew
of
a fi
gure
giv
en e
ach
ort
hog
onal
dra
win
g.
1.2.
Iden
tify
eac
h s
olid
.Nam
e th
e b
ases
,fac
es,e
dge
s,an
d v
erti
ces.
3.
trap
ezo
idal
pri
sm;
bas
es:
trap
ezo
id H
IJK
,tra
pez
oid
LM
NO
;fa
ces:
trap
ezo
id H
IJK
,tra
pez
oid
LM
NO
,�H
KLO
,�H
INO
,�IJ
MN
,�JK
LM;
edg
es:H�
I�,I�J�
,J�K�
,H�K�
,H�O�
,O�N�
,I�N�
,K�L�,
L�O�,L�
M�,J�
M�,M�
N�;
vert
ices
:H,I
,J,K
,L,M
,N,a
nd
O
4.
cylin
der
;b
ases
:ci
rcle
T,c
ircl
e Z
5.M
INER
ALS
Pyr
ite,
also
kn
own
as
fool
’s g
old,
can
for
m c
ryst
als
that
are
per
fect
cu
bes.
Su
ppos
e a
gem
olog
ist
wan
ts t
o cu
t a
cube
of
pyri
te t
o ge
t a
squ
are
and
a re
ctan
gula
rfa
ce.W
hat
cu
ts s
hou
ld b
e m
ade
to g
et e
ach
of
the
shap
es?
Illu
stra
te y
our
answ
ers.
a cu
t p
aral
lel t
o t
he
bas
es t
o
a cu
t th
rou
gh
dia
go
nal
ly o
pp
osi
te t
op
g
et a
sq
uar
ean
d b
ott
om
ed
ges
to
get
a r
ecta
ng
le
Z T
IJ
MH
K
NOL
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
back
vie
wco
rner
vie
w
top
view
left
view
front
vie
wrig
ht v
iew
Pra
ctic
e (
Ave
rag
e)
Th
ree-
Dim
ensi
on
al F
igu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
Answers (Lesson 12-1)
© Glencoe/McGraw-Hill A4 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csT
hre
e-D
imen
sio
nal
Fig
ure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill66
5G
lenc
oe G
eom
etry
Lesson 12-1
Pre-
Act
ivit
yW
hy
are
dra
win
gs o
f th
ree-
dim
ensi
onal
str
uct
ure
s va
luab
le t
oar
cheo
logi
sts?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-1 a
t th
e to
p of
pag
e 63
6 in
you
r te
xtbo
ok.
Wh
y do
you
th
ink
arch
eolo
gist
s w
ould
wan
t to
kn
ow t
he
deta
ils
of t
he
size
san
d sh
apes
of
anci
ent
thre
e-di
men
sion
al s
tru
ctu
res?
Sam
ple
an
swer
:T
his
info
rmat
ion
mig
ht
pro
vid
e cl
ues
ab
ou
t co
nst
ruct
ion
met
ho
ds
and
to
ols
an
d h
elp
arc
heo
log
ists
tra
ce a
dva
nce
s in
con
stru
ctio
n m
eth
od
s ov
er t
ime.
Rea
din
g t
he
Less
on
1.M
atch
eac
h d
escr
ipti
on f
rom
th
e fi
rst
colu
mn
wit
h o
ne
of t
he
term
s fr
om t
he
seco
nd
colu
mn
.(S
ome
of t
he
term
s m
ay b
e u
sed
mor
e th
an o
nce
or
not
at
all.)
a.a
poly
hed
ron
wit
h t
wo
para
llel
con
gru
ent
base
sv
b.
the
set
of p
oin
ts i
n s
pace
th
at a
re a
giv
en d
ista
nce
fro
m a
give
n p
oin
tvi
iic.
a re
gula
r po
lyh
edro
n w
ith
eig
ht
face
si
d.
a po
lyh
edro
n t
hat
has
all
fac
es b
ut
one
inte
rsec
tin
g at
on
epo
int
xie.
a li
ne
segm
ent
wh
ere
two
face
s of
a p
olyh
edro
n i
nte
rsec
tiv
f.a
soli
d w
ith
con
gru
ent
circ
ula
r ba
ses
in a
pai
r of
par
alle
lpl
anes
vii
g.a
regu
lar
poly
hed
ron
wh
ose
face
s ar
e sq
uar
esx
h.
a fl
at s
urf
ace
of a
pol
yhed
ron
ii
i.oc
tah
edro
nii
.fa
ceii
i.ic
osah
edro
niv
.ed
gev.
pris
mvi
.do
deca
hed
ron
vii.
cyli
nde
rvi
ii.s
pher
eix
.co
ne
x.h
exah
edro
nxi
.py
ram
idxi
i.te
trah
edro
n
2.F
ill
in t
he
mis
sin
g n
um
bers
,wor
ds,o
r ph
rase
s to
com
plet
e ea
ch s
ente
nce
.
a.A
tri
angu
lar
pris
m h
as
vert
ices
.It
has
fa
ces:
base
s ar
e co
ngr
uen
t
,an
d fa
ces
are
para
llel
ogra
ms.
b.
A r
egu
lar
octa
hed
ron
has
ve
rtic
es a
nd
face
s.E
ach
fac
e is
a(n
)
.
c.A
hex
agon
al p
rism
has
ve
rtic
es.I
t h
as
face
s:of
th
em a
re t
he
base
s,
wh
ich
are
con
gru
ent
,an
d th
e ot
her
fa
ces
are
para
llel
ogra
ms.
d.
An
oct
agon
al p
yram
id h
as
vert
ices
an
d fa
ces.
Th
e ba
se i
s a(
n)
,an
d th
e ot
her
fa
ces
are
.
e.T
her
e ar
e ex
actl
y ty
pes
of r
egu
lar
poly
hed
ra.T
hes
e ar
e ca
lled
th
e
soli
ds.A
pol
yhed
ron
wh
ose
face
s ar
e re
gula
r pe
nta
gon
s is
a
,wh
ich
has
fa
ces.
Hel
pin
g Y
ou
Rem
emb
er3.
A g
ood
way
to
rem
embe
r th
e ch
arac
teri
stic
s of
geo
met
ric
soli
ds i
s to
th
ink
abou
t h
owdi
ffer
ent
soli
ds a
re a
like
.Nam
e a
way
in
wh
ich
pyr
amid
s an
d co
nes
are
ali
ke.
Sam
ple
answ
er:T
hey
just
hav
e o
ne
bas
e an
d t
he
surf
aces
th
at a
re n
ot
the
bas
em
eet
at o
ne
po
int
(th
e ve
rtex
).12d
od
ecah
edro
nP
lato
nic
5tr
ian
gle
s8
oct
ago
n9
96
hex
ago
ns
28
12eq
uila
tera
l tri
ang
le8
63
tria
ng
les
25
6
©G
lenc
oe/M
cGra
w-H
ill66
6G
lenc
oe G
eom
etry
Dra
win
g S
olid
s o
n Is
om
etri
c D
ot
Pap
erIs
omet
ric
dot
pape
r is
hel
pfu
l fo
r dr
awin
g so
lids
.Rem
embe
r to
use
dash
ed l
ines
for
hid
den
edg
es.
For
eac
h s
olid
sh
own
,dra
w a
not
her
sol
id w
hos
e d
imen
sion
s ar
e tw
ice
as l
arge
.
1.2.
3.4.
5.6.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
Answers (Lesson 12-1)
© Glencoe/McGraw-Hill A5 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Net
s an
d S
urf
ace
Are
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill66
7G
lenc
oe G
eom
etry
Lesson 12-2
Mo
del
s fo
r Th
ree-
Dim
ensi
on
al F
igu
res
On
e w
ay t
o re
late
a t
hre
e-di
men
sion
alfi
gure
an
d a
two-
dim
ensi
onal
dra
win
g is
to
use
iso
met
ric
dot
pape
r.A
not
her
way
is
to m
ake
a fl
at p
atte
rn,c
alle
d a
net
,for
th
e su
rfac
es o
f a
soli
d.
Use
iso
met
ric
dot
pap
er t
o sk
etch
a t
rian
gula
r p
rism
wit
h 3
-4-5
rig
ht
tria
ngl
es a
s b
ases
an
d w
ith
a h
eigh
t of
3
un
its.
Ste
p 1
Dra
w A �
B�at
3 u
nit
s an
d dr
aw A�
C�at
4 u
nit
s.S
tep
2D
raw
A �D�
,B�E�
,an
d C�
F�,e
ach
at
3 u
nit
s.S
tep
3D
raw
B �C�
and
�D
EF
.
Mat
ch t
he
net
at
the
righ
t w
ith
on
e of
th
e so
lid
s b
elow
.
Th
e si
x sq
uar
es o
f th
e n
et c
an b
e fo
lded
in
to a
cu
be.T
he
net
rep
rese
nts
sol
id c
.
Sk
etch
eac
h s
olid
usi
ng
isom
etri
c d
ot p
aper
.
1.cu
be w
ith
edg
e 4
2.re
ctan
gula
r pr
ism
1 u
nit
hig
h,5
un
its
lon
g,an
d 4
un
its
wid
e
Dra
w a
net
for
eac
h s
olid
.
3.4.
5.6.
c.b
.a.
A
BC
D
EF
Exer
cises
Exer
cises
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
©G
lenc
oe/M
cGra
w-H
ill66
8G
lenc
oe G
eom
etry
Surf
ace
Are
aT
he
surf
ace
area
of a
sol
id i
s th
e su
m o
f th
e ar
eas
of t
he
face
s of
th
eso
lid.
Net
s ar
e u
sefu
l in
vis
ual
izin
g ea
ch f
ace
and
calc
ula
tin
g th
e ar
ea o
f th
e fa
ces.
Fin
d t
he
surf
ace
area
of
the
tria
ngu
lar
pri
sm.
Fir
st d
raw
a n
et u
sin
g re
ctan
gula
r do
t pa
per.
Usi
ng
the
Pyt
hag
orea
n T
heo
rem
,
the
hyp
oten
use
of
the
righ
t tr
ian
gle
is �
32�
4�
2 �or
5.
Su
rfac
e ar
ea�
A�
B�
C�
D�
E
��1 2� (
4 �
3) �
4 �
4 �
4 �
3 �
4 �
5 �
�1 2� (4
�3)
�60
squ
are
un
its
Fin
d t
he
surf
ace
area
of
each
sol
id.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
300
in2
820
cm2
3.4.
150
m2
363.
8 u
nit
s2
5.6.
224
un
its2
3350
un
its2
4025
2020
1518
8810
912
6
5 m
5 m5
m
24 c
m5
cm
10 c
m
12 in
.8
in.
5 in
.
A C
E
BD
44
3
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Net
s an
d S
urf
ace
Are
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 12-2)
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Net
s an
d S
urf
ace
Are
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill66
9G
lenc
oe G
eom
etry
Lesson 12-2
Sk
etch
eac
h s
olid
usi
ng
isom
etri
c d
ot p
aper
.
1.cu
be 2
un
its
on e
ach
edg
e2.
rect
angu
lar
pris
m 2
un
its
hig
h,
5 u
nit
s lo
ng,
and
2 u
nit
s w
ide
For
eac
h s
olid
,dra
w a
net
an
d f
ind
th
e su
rfac
e ar
ea.
3.S
amp
le n
et:
142
un
its2
4.S
amp
le n
et:
85 u
nit
s2
55
6
7
3
5
©G
lenc
oe/M
cGra
w-H
ill67
0G
lenc
oe G
eom
etry
Sk
etch
eac
h s
olid
usi
ng
isom
etri
c d
ot p
aper
.
1.re
ctan
gula
r pr
ism
3 u
nit
s h
igh
,2.
tria
ngu
lar
pris
m 3
un
its
hig
h,w
hos
e ba
ses
3 u
nit
s lo
ng,
and
2 u
nit
s w
ide
are
righ
t tr
ian
gles
wit
h l
egs
2 u
nit
s an
d 4
un
its
lon
g
3.F
or t
he
soli
d,dr
aw a
net
an
d fi
nd
the
surf
ace
area
.
Sam
ple
net
:34
2 u
nit
s2
4.SH
IPPI
NG
Raw
anda
nee
ds t
o w
rap
a pa
ckag
e to
sh
ip t
o h
er a
un
t.T
he
rect
angu
lar
pack
age
mea
sure
s 2
inch
es h
igh
,10
inch
es l
ong,
and
4 in
ches
wid
e.D
raw
a n
et o
f th
epa
ckag
e.H
ow m
uch
wra
ppin
g pa
per
does
Raw
anda
nee
d to
cov
er t
he
pack
age?
Sam
ple
net
:13
6 in
2
2
10
2
4
3
96
15
Pra
ctic
e (
Ave
rag
e)
Net
s an
d S
urf
ace
Are
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
Answers (Lesson 12-2)
© Glencoe/McGraw-Hill A7 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csN
ets
and
Su
rfac
e A
rea
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill67
1G
lenc
oe G
eom
etry
Lesson 12-2
Pre-
Act
ivit
yW
hy
is s
urf
ace
area
im
por
tan
t to
car
man
ufa
ctu
rers
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-2 a
t th
e to
p of
pag
e 64
3 in
you
r te
xtbo
ok.
Sup
pose
you
are
a p
asse
nger
in
a ca
r th
at i
s m
ovin
g at
50
mil
es p
er h
our
onth
e h
igh
way
.If
you
hol
d yo
ur
righ
t h
and
just
ou
tsid
e th
e ri
ght
win
dow
,in
wh
at p
osit
ion
doe
s yo
ur
han
d en
cou
nte
r th
e gr
eate
st a
ir r
esis
tan
ce?
pal
mo
f th
e h
and
op
en,w
ith
th
e ai
r h
itti
ng
th
e p
alm
at
a 90
°an
gle
Rea
din
g t
he
Less
on
1.N
ame
the
soli
d th
at c
an b
e fo
rmed
by
fold
ing
each
net
wit
hou
t an
y ov
erla
p.
a.b
.
rect
ang
ula
r p
rism
cylin
der
c.d
.
squ
are
pyr
amid
tetr
ahed
ron
2.S
upp
ly t
he
mis
sin
g n
um
ber,
wor
d,or
ph
rase
to
mak
e a
tru
e st
atem
ent.
Be
as s
peci
fic
aspo
ssib
le.
a.T
o fi
nd
the
surf
ace
area
of
a cu
be,a
dd t
he
area
s of
co
ngr
uen
t sq
uar
es.
b.
To
fin
d th
e su
rfac
e ar
ea o
f a
cyli
nde
r,ad
d th
e ar
eas
of t
wo
con
gru
ent
and
one
.
c.T
o fi
nd
the
surf
ace
area
of
a do
deca
hed
ron
,add
th
e ar
eas
of 1
2 co
ngr
uen
t
.
d.
To
fin
d th
e su
rfac
e ar
ea o
f an
ico
sah
edro
n,a
dd t
he
area
s of
co
ngr
uen
t
tria
ngl
es.
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
a m
ath
emat
ical
con
cept
is
to t
hin
k ab
out
how
th
e co
nce
ptre
late
s to
eve
ryda
y li
fe.H
ow c
ould
you
exp
lain
th
e co
nce
pt o
f su
rfac
e ar
eau
sin
g an
ever
yday
sit
uat
ion
?S
amp
le a
nsw
er:T
he
surf
ace
area
of
a so
lid s
hap
e te
lls y
ou
ho
w m
uch
wra
pp
ing
pap
er y
ou
wo
uld
nee
d t
o w
rap
a p
rese
nt
wit
h t
hat
sh
ape
and
size
.equ
ilate
ral
20p
enta
go
ns
reg
ula
r
rect
ang
leci
rcle
s
6
©G
lenc
oe/M
cGra
w-H
ill67
2G
lenc
oe G
eom
etry
Pyr
amid
s
1.O
n a
sh
eet
of p
aper
,dra
w t
he
figu
re a
t th
e ri
ght
so t
hat
th
e m
easu
rem
ents
are
acc
ura
te.
Cu
t ou
t th
e sh
ape
and
fold
it
to m
ake
a py
ram
id.
See
stu
den
ts’w
ork
.
2.M
easu
re t
he
hei
ght
from
th
e h
igh
est
poin
t st
raig
ht
dow
n (
perp
endi
cula
r) t
o th
e ba
se.
Wh
at i
s th
e h
eigh
t of
th
e py
ram
id?
12 c
m
Th
e d
raw
ing
at t
he
righ
t sh
ows
the
pyr
amid
you
mad
e.A
nsw
er e
ach
of
the
foll
owin
g.
3.M
easu
re t
he
len
gth
of
yin
you
r py
ram
id.
5 cm
4.M
easu
re t
he
len
gth
of
z,th
e h
eigh
t of
on
e of
th
e tr
ian
gula
r fa
ces.
13 c
m
5.U
se t
he
Pyt
hag
orea
n T
heo
rem
to
fin
d x,
the
hei
ght
of t
he
pyra
mid
.Is
th
is e
qual
to
the
hei
ght
of y
our
mod
el?
12 c
m;
yes
Mak
e a
pap
er p
atte
rn f
or e
ach
pyr
amid
bel
ow.C
ut
out
you
r p
atte
rn a
nd
fol
d i
t to
mak
e a
mod
el.M
easu
re t
he
hei
ght
of t
he
pyr
amid
an
d u
se t
he
Pyt
hag
orea
nT
heo
rem
to
veri
fy t
his
mea
sure
.
6.3
cm7.
12 c
m
12.5
cm
7 cm
5 cm
8 cm
y
xz
10 c
m
13 cm
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
Answers (Lesson 12-2)
© Glencoe/McGraw-Hill A8 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Su
rfac
e A
reas
of
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill67
3G
lenc
oe G
eom
etry
Lesson 12-3
Late
ral A
reas
of
Pris
ms
Her
e ar
e so
me
char
acte
rist
ics
of p
rism
s.
•T
he
base
s ar
e pa
rall
el a
nd
con
gru
ent.
•T
he
late
ral
face
sar
e th
e fa
ces
that
are
not
bas
es.
•T
he
late
ral
face
s in
ters
ect
at l
ater
al e
dge
s,w
hic
h a
re p
aral
lel.
•T
he
alti
tud
eof
a p
rism
is
a se
gmen
t th
at i
s pe
rpen
dicu
lar
to t
he
base
s w
ith
an
en
dpoi
nt
in e
ach
bas
e.•
For
a r
igh
t p
rism
,th
e la
tera
l ed
ges
are
perp
endi
cula
r to
th
e ba
ses.
Oth
erw
ise,
the
pris
m i
s ob
liq
ue.
Lat
eral
Are
a If
a pr
ism
has
a la
tera
l are
a of
Lsq
uare
uni
ts,
a he
ight
of
hun
its,
of
a P
rism
and
each
bas
e ha
s a
perim
eter
of
Pun
its,
then
L�
Ph.
Fin
d t
he
late
ral
area
of
the
regu
lar
pen
tago
nal
pri
sm a
bov
e if
eac
hb
ase
has
a p
erim
eter
of
75 c
enti
met
ers
and
th
e al
titu
de
is 1
0 ce
nti
met
ers.
L�
Ph
Late
ral a
rea
of a
pris
m
�75
(10)
P�
75,
h�
10
�75
0M
ultip
ly.
Th
e la
tera
l ar
ea i
s 75
0 sq
uar
e ce
nti
met
ers.
Fin
d t
he
late
ral
area
of
each
pri
sm.
1.2.
120
m2
540
in2
(10
in.�
8 in
.bas
e)
3.4.
540
in2
588
cm2
5.6.
128
in2
(rec
tan
gu
lar
bas
e)38
4 m
2
192
in2
(sq
uar
e b
ase)
4 m
16 m
4 in
.
4 in
.
12 in
.
20 c
m
10 c
m10
cm
12 c
m9
cm
6 in
.18
in.
460
in2
(8 in
.�15
in.b
ase)
;40
0 in
2
(10
in.�
15 in
.bas
e);
15 in
.
10 in
.
8 in
.4
m
3 m
10 m
pent
agon
al p
rismal
titud
e
late
ral
edge
late
ral
face
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill67
4G
lenc
oe G
eom
etry
Surf
ace
Are
as o
f Pr
ism
sT
he
surf
ace
area
of
a pr
ism
is
the
late
ral
area
of
the
pris
m p
lus
the
area
s of
th
e ba
ses.
Su
rfac
e A
rea
If th
e to
tal s
urfa
ce a
rea
of a
pris
m is
Tsq
uare
uni
ts,
its h
eigh
t is
of
a P
rism
hun
its,
and
each
bas
e ha
s an
are
a of
Bsq
uare
uni
ts a
nd a
pe
rimet
er o
f P
units
, th
en T
�L
�2B
.
Fin
d t
he
surf
ace
area
of
the
tria
ngu
lar
pri
sm a
bov
e.F
ind
the
late
ral
area
of
the
pris
m.
L�
Ph
Late
ral a
rea
of a
pris
m
�(1
8)(1
0)P
�18
, h
�10
�18
0 cm
2M
ultip
ly.
Fin
d th
e ar
ea o
f ea
ch b
ase.
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
the
hei
ght
of t
he
tria
ngu
lar
base
.
h2
�32
�62
Pyt
hago
rean
The
orem
h2
�27
Sim
plify
.
h�
3�3�
Take
the
squ
are
root
of
each
sid
e.
B�
�1 2��
base
�h
eigh
tA
rea
of a
tria
ngle
��1 2� (
6)(3
�3�)
or 1
5.6
cm2
Th
e to
tal
area
is
the
late
ral
area
plu
s th
e ar
ea o
f th
e tw
o ba
ses.
T�
180
�2(
15.6
)S
ubst
itutio
n
�21
1.2
cm2
Sim
plify
.
Fin
d t
he
surf
ace
area
of
each
pri
sm.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
3.
1024
in2
84 m
232
4 m
2
4.5.
6.
619.
1 in
241
5.4
in2
384
m2
8 m
8 m
8 m
8 in
.
8 in
.
8 in
.
15 in
.6
in.
12 in
.
12 m
5 m
6 m
3 m
6 m
4 m
24 in
.
10 in
.
8 in
.
6 cm
6 cm
6 cm
10 c
mh
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Su
rfac
e A
reas
of
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 12-3)
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Su
rfac
e A
reas
of
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill67
5G
lenc
oe G
eom
etry
Lesson 12-3
Fin
d t
he
late
ral
area
of
each
pri
sm.
1.2.
480
un
its2
(sq
uar
e b
ase)
240
un
its2
(8 �
12 b
ase)
528
un
its2
(rec
tan
gu
lar
bas
e)28
8 u
nit
s2(1
2 �
6 b
ase)
336
un
its2
(8 �
6 b
ase)
3.4.
120
un
its2
324
un
its2
Fin
d t
he
surf
ace
area
of
each
pri
sm.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
5.6.
600
un
its2
782
un
its2
7.8.
312.
2 u
nit
s285
.2 u
nit
s27
4
39
610
15
7
13
18
8
6
9
9
9
12
1056
8
8
6
12
12
12
10
©G
lenc
oe/M
cGra
w-H
ill67
6G
lenc
oe G
eom
etry
Fin
d t
he
late
ral
area
of
each
pri
sm.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
1920
un
its2
(sq
uar
e b
ase)
224.
3 u
nit
s214
10 u
nit
s2(r
ecta
ng
ula
r b
ase)
3.4.
132
un
its2
123.
5 u
nit
s2
Fin
d t
he
surf
ace
area
of
each
pri
sm.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
5.6.
514
un
its2
311.
2 u
nit
s2
7.8.
263.
7 u
nit
s216
80 u
nit
s2
9.C
RA
FTS
Bec
ca m
ade
a re
ctan
gula
r je
wel
ry b
ox in
her
art
cla
ss a
nd p
lans
to
cove
r it
in r
ed
silk
.If
the
jew
elry
box
is
6�1 2�
inch
es l
ong,
4 �1 2�
inch
es w
ide,
and
3 in
ches
hig
h,f
ind
the
surf
ace
area
th
at w
ill
be c
over
ed.
124�
1 2�in
2
14
14
23
9
95
6
13
79
4
17
4
4
9.5
52
11
8
105
15
15
32
Pra
ctic
e (
Ave
rag
e)
Su
rfac
e A
reas
of
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
Answers (Lesson 12-3)
© Glencoe/McGraw-Hill A10 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csS
urf
ace
Are
as o
f P
rism
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill67
7G
lenc
oe G
eom
etry
Lesson 12-3
Pre-
Act
ivit
yH
ow d
o b
rick
mas
ons
kn
ow h
ow m
any
bri
cks
to o
rder
for
a p
roje
ct?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-3 a
t th
e to
p of
pag
e 64
9 in
you
r te
xtbo
ok.
How
cou
ld t
he
bric
k m
ason
fig
ure
ou
t ap
prox
imat
ely
how
man
y br
icks
are
nee
ded
for
the
gara
ge?
Sam
ple
an
swer
:F
ind
th
e ar
ea o
f ea
ch w
all
of
the
gar
age
and
ad
d t
hes
e ar
eas.
Div
ide
this
to
tal a
rea
by t
he
area
of
on
e fa
ce o
f a
bri
ck,b
ut
take
into
acc
ou
nt
the
amo
un
to
f sp
ace
for
the
mo
rtar
bet
wee
n t
he
bri
cks.
Rea
din
g t
he
Less
on
1.D
eter
min
e w
het
her
eac
h s
ente
nce
is
alw
ays,
som
etim
es,o
r n
ever
tru
e.
a.A
bas
e of
a p
rism
is
a fa
ce o
f th
e pr
ism
.al
way
sb
.A
fac
e of
a p
rism
is
a ba
se o
f th
e pr
ism
.so
met
imes
c.T
he
late
ral
face
s of
a p
rism
are
rec
tan
gles
.so
met
imes
d.
If a
bas
e of
a p
rism
has
nve
rtic
es,t
hen
th
e pr
ism
has
nfa
ces.
nev
ere.
If a
bas
e of
a p
rism
has
nve
rtic
es,t
hen
th
e pr
ism
has
nla
tera
l ed
ges.
alw
ays
f.In
a r
igh
t pr
ism
,th
e la
tera
l ed
ges
are
also
alt
itu
des.
alw
ays
g.T
he
base
s of
a p
rism
are
con
gru
ent
regu
lar
poly
gon
s.so
met
imes
h.
An
y tw
o la
tera
l ed
ges
of a
pri
sm a
re p
erpe
ndi
cula
r to
eac
h o
ther
.n
ever
i.In
a r
ecta
ngu
lar
pris
m,a
ny
pair
of
oppo
site
fac
es c
an b
e ca
lled
th
e ba
ses.
alw
ays
j.A
ll o
f th
e la
tera
l fa
ces
of a
pri
sm a
re c
ongr
uen
t to
eac
h o
ther
.so
met
imes
2.E
xpla
in t
he
diff
eren
ce b
etw
een
th
e la
tera
l ar
eaof
a p
rism
an
d th
e su
rfac
e ar
eaof
apr
ism
.You
r ex
plan
atio
n s
hou
ld a
pply
to
both
rig
ht
and
obli
que
pris
ms.
Do
not
use
an
yfo
rmu
las
in y
our
expl
anat
ion
.S
amp
le a
nsw
er:T
he
late
ral a
rea
is t
he
sum
of
the
area
s o
f la
tera
l fac
es.T
he
surf
ace
area
is t
he
sum
of
the
area
s o
f al
lth
e fa
ces,
incl
ud
ing
bo
th t
he
late
ral f
aces
an
d t
he
bas
es.
3.R
efer
to
the
figu
re.
a.N
ame
this
sol
id w
ith
as
spec
ific
a n
ame
as p
ossi
ble.
rig
ht
pen
tag
on
al p
rism
b.
Nam
e th
e ba
ses
of t
he
soli
d.p
enta
go
ns
AB
CD
Ean
d F
GH
IJc.
Nam
e th
e la
tera
l fa
ces.
rect
ang
les
AB
GF
,BC
HG
,CD
IH,D
EJI
,an
d E
AF
Jd
.N
ame
the
edge
s.A�
F�,B�
G�,C�
H�,D�
I�,E�
J�,A�
B�,B�
C�,C�
D�,D�
E�,E�
A�,F�
G�,G�
H�,H�
I�,I�J�
,J�F�
e.N
ame
an a
ltit
ude
of
the
soli
d.A�
F�,B�
G�,C�
H�,D�
I�,o
r E�
J�f.
If a
repr
esen
ts t
he
area
,Pre
pres
ents
th
e pe
rim
eter
of
one
of t
he
base
s,an
d x
�A
F,
wri
te a
n ex
pres
sion
for
the
sur
face
are
a of
the
sol
id t
hat
invo
lves
a,P
,and
x.
Px
�2a
Hel
pin
g Y
ou
Rem
emb
er4.
A g
ood
way
to
rem
embe
r a
new
mat
hem
atic
al t
erm
is
to r
elat
e it
to
an e
very
day
use
of
the
sam
e w
ord.
How
can
th
e w
ay t
he
wor
d la
tera
lis
use
d in
spo
rts
hel
p yo
u r
emem
ber
the
mea
nin
g of
th
e la
tera
l ar
eaof
a s
olid
?S
amp
le a
nsw
er:
In f
oo
tbal
l,a
pas
sth
row
n t
o t
he
sid
eis
cal
led
a la
tera
l pas
s.In
geo
met
ry,t
he
late
ral a
rea
isth
e “s
ide
area
,”o
r th
e su
m o
f th
e ar
eas
of
all t
he
sid
e su
rfac
es o
f th
eso
lid (
the
surf
aces
oth
er t
han
th
e b
ases
).
A
BC
D IF
E
GH
J
©G
lenc
oe/M
cGra
w-H
ill67
8G
lenc
oe G
eom
etry
Cro
ss S
ecti
on
s o
f P
rism
sW
hen
a p
lan
e in
ters
ects
a s
olid
fig
ure
to
form
a
two-
dim
ensi
onal
fig
ure
,th
e re
sult
s is
cal
led
a cr
oss
sect
ion
.Th
e fi
gure
at
the
righ
t sh
ows
a pl
ane
inte
rsec
tin
g a
cube
.Th
e cr
oss
sect
ion
is
a h
exag
on.
For
eac
h r
igh
t p
rism
,con
nec
t th
e la
bel
ed p
oin
ts i
n a
lph
abet
ical
or
der
to
show
a c
ross
sec
tion
.Th
en i
den
tify
th
e p
olyg
on.
1.2.
3.
rect
ang
letr
ian
gle
trap
ezo
id
Ref
er t
o th
e ri
ght
pri
sms
show
n a
t th
e ri
ght.
In t
he
rect
angu
lar
pri
sm,A
and
Car
e m
idp
oin
ts.I
den
tify
th
e cr
oss-
sect
ion
p
olyg
on f
orm
ed b
y a
pla
ne
con
tain
ing
the
give
n p
oin
ts.
4.A
,C,H
rect
ang
le
5.C
,E,G
tria
ng
le
6.H
,C,E
,Ftr
apez
oid
7.H
,A,E
pen
tag
on
8.B
,D,F
rect
ang
le
9.V
,X,R
tria
ng
le
10.R
,T,Y
rect
ang
le
11.R
,S,W
trap
ezo
id
A
B HG
F
DC
E
VXS
U
Y
Z
R
T
W
AB
CD
X
Y Z
S
R
U
T
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
Answers (Lesson 12-3)
© Glencoe/McGraw-Hill A11 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Su
rfac
e A
reas
of
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill67
9G
lenc
oe G
eom
etry
Lesson 12-4
Late
ral A
reas
of
Cyl
ind
ers
A c
ylin
der
is a
sol
id w
hos
e ba
ses
are
con
gru
ent
circ
les
that
lie
in
par
alle
l pl
anes
.Th
e ax
isof
a c
ylin
der
is t
he
segm
ent
wh
ose
endp
oin
ts a
re t
he
cen
ters
of
thes
e ci
rcle
s.F
or a
rig
ht
cyli
nd
er,t
he
axis
an
d th
e al
titu
de o
f th
e cy
lin
der
are
equ
al.T
he
late
ral
area
of
a ri
ght
cyli
nde
r is
th
eci
rcu
mfe
ren
ce o
f th
e cy
lin
der
mu
ltip
lied
by
the
hei
ght.
Lat
eral
Are
a If
a cy
linde
r ha
s a
late
ral a
rea
of L
squa
re u
nits
, a
heig
ht o
f h
units
, o
f a
Cyl
ind
eran
d th
e ba
ses
have
rad
ii of
run
its,
then
L�
2�rh
.
Fin
d t
he
late
ral
area
of
the
cyli
nd
er a
bov
e if
th
e ra
diu
s of
th
e b
ase
is 6
cen
tim
eter
s an
d t
he
hei
ght
is 1
4 ce
nti
met
ers.
L�
2�rh
Late
ral a
rea
of a
cyl
inde
r
�2�
(6)(
14)
Sub
stitu
tion
�52
7.8
Sim
plify
.
Th
e la
tera
l ar
ea i
s ab
out
527.
8 sq
uar
e ce
nti
met
ers.
Fin
d t
he
late
ral
area
of
each
cyl
ind
er.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
301.
6 cm
237
7.0
in2
3.4.
113.
1 cm
250
2.7
cm2
5.6.
150.
8 m
212
.6 m
2
2 m
1 m
12 m
4 m
20 c
m
8 cm
6 cm
3 cm
3 cm
6 in
.10
in.
12 c
m
4 cm
radi
us o
f bas
eax
is
base
base
heig
ht
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill68
0G
lenc
oe G
eom
etry
Surf
ace
Are
as o
f C
ylin
der
sT
he
surf
ace
area
of
a cy
lin
der
is t
he
late
ral
area
of
the
cyli
nde
r pl
us
the
area
s of
th
e ba
ses.
Su
rfac
e A
rea
If a
cylin
der
has
a su
rfac
e ar
ea o
f T
squa
re u
nits
, a
heig
ht o
f o
f a
Cyl
ind
erh
units
, an
d th
e ba
ses
have
rad
ii of
run
its,
then
T�
2�rh
�2�
r2.
Fin
d t
he
surf
ace
area
of
the
cyli
nd
er.
Fin
d th
e la
tera
l ar
ea o
f th
e cy
lin
der.
If t
he
diam
eter
is
12 c
enti
met
ers,
then
th
e ra
diu
s is
6 c
enti
met
ers.
L�
Ph
Late
ral a
rea
of a
cyl
inde
r
�(2
�r)
hP
�2�
r
�2�
(6)(
14)
r�
6, h
�14
�52
7.8
Sim
plify
.
Fin
d th
e ar
ea o
f ea
ch b
ase.
B�
�r2
Are
a of
a c
ircle
��
(6)2
r�
6
�11
3.1
Sim
plify
.
Th
e to
tal
area
is
the
late
ral
area
plu
s th
e ar
ea o
f th
e tw
o ba
ses.
T�
527.
8 �
113.
1 �
113.
1 or
754
squ
are
cen
tim
eter
s.
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
603.
2 in
250
.3 m
2
3.4.
94.2
yd
210
05.3
in2
5.6.
213.
6 m
214
07.4
in2
20 in
.
8 in
.
2 m
15 m
8 in
.
12 in
.
2 yd
3 yd
2 m
2 m
12 in
.
10 in
.
14 c
m
12 c
m
base
base
late
ral a
rea
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Su
rfac
e A
reas
of
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 12-4)
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Su
rfac
e A
reas
of
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill68
1G
lenc
oe G
eom
etry
Lesson 12-4
Fin
d t
he
surf
ace
area
of
a cy
lin
der
wit
h t
he
give
n d
imen
sion
s.R
oun
d t
o th
en
eare
st t
enth
.
1.r
�10
in
.,h
�12
in
.2.
r�
8 cm
,h�
15 c
m
1382
.3 in
211
56.1
cm
2
3.r
�5
ft,h
�20
ft
4.d
�20
yd,
h�
5 yd
785.
4 ft
294
2.5
yd2
5.d
�8
m,h
�7
m6.
d�
24 m
m,h
�20
mm
276.
5 m
224
12.7
mm
2
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.R
oun
d t
o th
e n
eare
st t
enth
.
7.8.
377.
0 ft
213
1.9
cm2
Fin
d t
he
rad
ius
of t
he
bas
e of
eac
h c
ylin
der
.
9.T
he
surf
ace
area
is
603.
2 sq
uar
e m
eter
s,an
d th
e h
eigh
t is
10
met
ers.
6 m
10.T
he
surf
ace
area
is
100.
5 sq
uar
e in
ches
,an
d th
e h
eigh
t is
6 i
nch
es.
2 in
.
11.T
he
surf
ace
area
is
226.
2 sq
uar
e ce
nti
met
ers,
and
the
hei
ght
is 5
cen
tim
eter
s.
4 cm
12.T
he
surf
ace
area
is
1520
.5 s
quar
e ya
rds,
and
the
hei
ght
is 1
4.2
yard
s.
10 y
d
4 m
8.5
m
5 ft 7
ft
©G
lenc
oe/M
cGra
w-H
ill68
2G
lenc
oe G
eom
etry
Fin
d t
he
surf
ace
area
of
a cy
lin
der
wit
h t
he
give
n d
imen
sion
s.R
oun
d t
o th
en
eare
st t
enth
.
1.r
�8
cm,h
�9
cm2.
r�
12 i
n.,
h�
14 i
n.
854.
5 cm
219
60.4
in2
3.d
�14
mm
,h�
32 m
m4.
d�
6 yd
,h�
12 y
d
1715
.3 m
m2
282.
7 yd
2
5.r
�2.
5 ft
,h�
7 ft
6.d
�13
m,h
�20
m
149.
2 ft
210
82.3
m2
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.R
oun
d t
o th
e n
eare
st t
enth
.
7.8.
1581
.8 in
231
66.7
m2
Fin
d t
he
rad
ius
of t
he
bas
e of
eac
h r
igh
t cy
lin
der
.
9.T
he
surf
ace
area
is
628.
3 sq
uar
e m
illi
met
ers,
and
the
hei
ght
is 1
5 m
illi
met
ers.
5 m
m
10.T
he
surf
ace
area
is
892.
2 sq
uar
e fe
et,a
nd
the
hei
ght
is 4
.2 f
eet.
10 f
t
11.T
he
surf
ace
area
is
158.
3 sq
uar
e in
ches
,an
d th
e h
eigh
t is
5.4
in
ches
.
3 in
.
12.K
ALE
IDO
SCO
PES
Nat
han
bu
ilt
a ka
leid
osco
pe w
ith
a 2
0-ce
nti
met
er b
arre
l an
d a
5-ce
nti
met
er d
iam
eter
.He
plan
s to
cov
er t
he
barr
el w
ith
em
boss
ed p
aper
of
his
ow
nde
sign
.How
man
y sq
uar
e ce
nti
met
ers
of p
aper
wil
l it
tak
e to
cov
er t
he
barr
el o
f th
eka
leid
osco
pe?
abo
ut
314.
2 cm
2
12 m
30 m
19 in
.
17 in
.
Pra
ctic
e (
Ave
rag
e)
Su
rfac
e A
reas
of
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
Answers (Lesson 12-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
urf
ace
Are
as o
f C
ylin
der
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill68
3G
lenc
oe G
eom
etry
Lesson 12-4
Pre-
Act
ivit
yH
ow a
re c
ylin
der
s u
sed
in
ext
rem
e sp
orts
?R
ead
the
intr
oduc
tion
to
Les
son
12-4
at
the
top
of p
age
655
in y
our
text
book
.
Wh
y is
th
e su
rfac
e ar
ea o
f a
hal
f-pi
pe m
ore
than
hal
f th
e su
rfac
e ar
ea o
f a
com
plet
e pi
pe?
Sam
ple
an
swer
:Th
e su
rfac
e ar
ea o
f th
e h
alf-
pip
e in
clu
des
an
add
ed f
lat
sect
ion
in t
he
mid
dle
.
Rea
din
g t
he
Less
on
1.U
nde
rlin
e th
e co
rrec
t w
ord
or p
hra
se t
o fo
rm a
tru
e st
atem
ent.
a.T
he
base
s of
a c
ylin
der
are
(rec
tan
gles
/reg
ula
r po
lygo
ns/
circ
les)
.
b.
Th
e (a
xis/
radi
us/
diam
eter
) of
a c
ylin
der
is t
he
segm
ent
wh
ose
endp
oin
ts a
re t
he
cen
ters
of
the
base
s.
c.T
he
net
of
a cy
lin
der
is c
ompo
sed
of t
wo
con
gru
ent
(rec
tan
gles
/cir
cles
) an
d on
e(r
ecta
ngl
e/se
mic
ircl
e).
d.
In a
rig
ht
cyli
nde
r,th
e ax
is o
f th
e cy
lin
der
is a
lso
a(n
) (b
ase/
late
ral
edge
/alt
itu
de).
e.A
cyl
inde
r th
at i
s n
ot a
rig
ht
cyli
nde
r is
cal
led
an (
acu
te/o
btu
se/o
bliq
ue)
cyl
inde
r.
2.M
atch
eac
h d
escr
ipti
on f
rom
th
e fi
rst
colu
mn
wit
h a
n e
xpre
ssio
n f
rom
th
e se
con
d co
lum
nth
at r
epre
sen
ts i
ts v
alu
e.a.
the
late
ral
area
of
a ri
ght
cyli
nde
r in
wh
ich
th
e ra
diu
s of
each
bas
e is
xcm
an
d th
e le
ngt
h o
f th
e ax
is i
s y
cmv
b.
the
surf
ace
area
of
a ri
ght
pris
m w
ith
squ
are
base
s in
wh
ich
the
len
gth
of
a si
de o
f a
base
is
xcm
an
d th
e le
ngt
h o
f a
late
ral
edge
is
ycm
ic.
the
surf
ace
area
of
a ri
ght
cyli
nde
r in
wh
ich
th
e ra
diu
s of
aba
se i
s x
cm a
nd
the
hei
ght
is y
cmii
d.
the
surf
ace
area
of
regu
lar
hex
ahed
ron
(cu
be)
in w
hic
h t
he
len
gth
of
each
edg
e is
xcm
ive.
the
late
ral
area
of
a tr
ian
gula
r pr
ism
in
wh
ich
th
e ba
ses
are
equ
ilat
eral
tri
angl
es w
ith
sid
e le
ngt
h x
cm a
nd
the
hei
ght
isy
cmiii
f.th
e su
rfac
e ar
ea o
f a
righ
t cy
lin
der
in w
hic
h t
he
diam
eter
of
the
base
is
xcm
an
d th
e le
ngt
h o
f th
e ax
is i
s y
cmvi
i.(2
x2�
4xy)
cm
2
ii.(
2�xy
�2�
x2)
cm2
iii.
3xy
cm2
iv.
6x2
cm2
v.2�
xycm
2
vi. ���
2x2 ��
�xy
�cm
2
Hel
pin
g Y
ou
Rem
emb
er3.
Oft
en t
he
best
way
to
rem
embe
r a
mat
hem
atic
al f
orm
ula
is
to t
hin
k ab
out
wh
ere
the
diff
eren
t pa
rts
of t
he f
orm
ula
com
e fr
om.H
ow c
an y
ou u
se t
his
appr
oach
to
rem
embe
r th
efo
rmul
a fo
r th
e su
rfac
e ar
ea o
f a
cyli
nder
?S
amp
le a
nsw
er:T
hin
k ab
ou
t th
e n
et f
or
a cy
lind
er.T
he
two
bas
es a
re c
ircl
es,e
ach
wit
h r
adiu
s r,
so t
he
sum
of
thei
r ar
eas
is 2
�r2
.Th
e la
tera
l su
rfac
e is
a r
ecta
ng
le w
ho
se d
imen
sio
ns
are
the
circ
um
fere
nce
2�
ro
f th
e ci
rcu
lar
bas
e an
d t
he
hei
gh
t h
of
the
cylin
der
,so
th
e la
tera
l are
a is
2�
rh.A
dd
th
e la
tera
l are
a an
d t
he
area
of
the
two
bas
es t
o g
et t
he
surf
ace
area
of
the
cylin
der
:2�
rh�
2�r2
.
©G
lenc
oe/M
cGra
w-H
ill68
4G
lenc
oe G
eom
etry
Can
-did
ly S
pea
kin
gB
ever
age
com
pan
ies
hav
e m
ath
emat
ical
ly d
eter
min
ed t
he
idea
l sh
ape
for
a 12
-ou
nce
sof
t-dr
ink
can
.Wh
y w
on't
any
shap
e do
? S
ome
shap
es a
re m
ore
econ
omic
al t
han
oth
ers.
In o
rder
to
hol
d 12
ou
nce
s of
sof
t dr
ink,
an e
xtre
mel
ysk
inn
y ca
n w
ould
hav
e to
be
very
tal
l.T
he
tota
l am
oun
t of
alu
min
um
use
d fo
rsu
ch a
sh
ape
wou
ld b
e gr
eate
r th
an t
he
amou
nt
use
d fo
r th
e co
nve
nti
onal
sh
ape,
thu
s co
stin
g th
e co
mpa
ny
mor
e to
mak
e th
e sk
inn
y ca
n.T
he
radi
us
rch
osen
dete
rmin
es t
he
hei
ght
hn
eede
d to
hol
d 12
ou
nce
s of
liq
uid
.Th
is a
lso
dete
rmin
esth
e am
oun
t of
alu
min
um
nee
ded
to m
ake
the
can
.Com
pan
ies
also
hav
e to
kee
pin
min
d th
at t
he
top
of t
he
can
is
thre
e ti
mes
th
icke
r th
an t
he
bott
om a
nd
side
s.W
hy?
So
you
won
’t te
ar o
ff t
he
enti
re t
op w
hen
you
ope
n t
he
can
! Th
e fo
llow
ing
form
ula
s ca
n b
e u
sed
to f
ind
the
hei
ght
and
amou
nt
of a
lum
inu
m a
nee
ded
for
a12
-ou
nce
sof
t-dr
ink
can
.
h �
�1 �7.r8 29�
a �
0.02
���r2
�r35
.78
��
The
val
ues
of r
and
har
e m
easu
red
in in
ches
.
Fin
d t
he
hei
ght
nee
ded
for
a 1
2-ou
nce
can
for
eac
h r
adiu
s.R
oun
d t
o th
e n
eare
st t
enth
.
1.2�
2 3�in
.0.
8 in
.2.
1 in
.5.
7 in
.3.
3 in
.0.
6 in
.4.
1�3 4�
in.
1.9
in.
Sk
etch
th
e sh
ape
of e
ach
can
in
Exe
rcis
es 1
–4.
5.E
xerc
ise
16.
Exe
rcis
e 2
7.E
xerc
ise
38.
Exe
rcis
e 4
9.a.
Mea
sure
th
e ra
diu
s of
a s
oft-
drin
k ca
n.
1�1 8�
in.
b.
Use
th
e fo
rmu
la t
o fi
nd
the
hei
ght
of t
he
can
.4
�1 2�in
.
c.M
easu
re t
he
hei
ght
of a
sof
t-dr
ink
can
.�
4�3 4�
in.
d.H
ow d
oes
this
mea
sure
com
pare
to
you
r fi
ndi
ngs
in
par
t a?
See
stu
den
ts’w
ork
.
10.F
ind
the
amou
nt
of a
lum
inu
m u
sed
in m
akin
g a
soft
-dri
nk
can
.�
2.3
oz
13 – 4 in.
1.9
in.
3 in
. 0.6
in.
5.7
in.
1 in
.
0.8
in.
22 – 3 in.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
Answers (Lesson 12-4)
© Glencoe/McGraw-Hill A14 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Su
rfac
e A
reas
of
Pyr
amid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill68
5G
lenc
oe G
eom
etry
Lesson 12-5
Late
ral A
reas
of
Reg
ula
r Py
ram
ids
Her
e ar
e so
me
prop
erti
es o
f py
ram
ids.
•T
he
base
is
a po
lygo
n.
•A
ll o
f th
e fa
ces,
exce
pt t
he
base
,in
ters
ect
in a
com
mon
poi
nt
know
n a
s th
e ve
rtex
.•
Th
e fa
ces
that
in
ters
ect
at t
he
vert
ex,w
hic
h a
re c
alle
d la
tera
l fa
ces,
are
tria
ngl
es.
For
a r
egu
lar
pyr
amid
,th
e ba
se i
s a
regu
lar
poly
gon
an
d th
e sl
ant
hei
ght
is t
he
hei
ght
of e
ach
lat
eral
fac
e.
Lat
eral
Are
a o
f a
If a
regu
lar
pyra
mid
has
a la
tera
l are
a of
Lsq
uare
uni
ts,
a sl
ant
heig
ht o
f �
units
, R
egu
lar
Pyr
amid
and
its b
ase
has
a pe
rimet
er o
f P
units
, th
en L
��1 2� P
�.
Th
e ro
of o
f a
bar
n i
s a
regu
lar
octa
gon
al
pyr
amid
.Th
e b
ase
of t
he
pyr
amid
has
sid
es o
f 12
fee
t,an
d t
he
slan
t h
eigh
t of
th
e ro
of i
s 15
fee
t.F
ind
th
e la
tera
l ar
ea o
f th
e ro
of.
Th
e pe
rim
eter
of
the
base
is
8(12
) or
96
feet
.
L�
�1 2� P�
Late
ral a
rea
of a
pyr
amid
��1 2� (
96)(
15)
P�
96,
��
15
�72
0M
ultip
ly.
Th
e la
tera
l ar
ea i
s 72
0 sq
uar
e fe
et.
Fin
d t
he
late
ral
area
of
each
reg
ula
r p
yram
id.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
180
cm2
70 f
t2
3.4.
2100
m2
62.4
ft2
5.6.
701.
5 in
221
6 yd
2
45�
12 y
d60
�18
in.
60�
6 ft
42 m
20 m
3.5
ft
10 ft
8 cm
8 cm
8 cm
15 c
m
base
late
ral e
dge
late
ral f
ace
verte
x
slan
t hei
ght
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill68
6G
lenc
oe G
eom
etry
Surf
ace
Are
as o
f R
egu
lar
Pyra
mid
sT
he
surf
ace
area
of
a r
egu
lar
pyra
mid
is
the
late
ral
area
plu
s th
e ar
ea o
f th
e ba
se.
Su
rfac
e A
rea
of
aIf
a re
gula
r py
ram
id h
as a
sur
face
are
a of
Tsq
uare
uni
ts,
Reg
ula
r P
yram
ida
slan
t he
ight
of
�un
its,
and
its b
ase
has
a pe
rimet
er o
f P
units
and
an
area
of
Bsq
uare
uni
ts,
then
T�
�1 2� P�
�B
.
For
th
e re
gula
r sq
uar
e p
yram
id a
bov
e,fi
nd
th
e su
rfac
e ar
ea t
o th
en
eare
st t
enth
if
each
sid
e of
th
e b
ase
is 1
2 ce
nti
met
ers
and
th
e h
eigh
t of
th
ep
yram
id i
s 8
cen
tim
eter
s.L
ook
at t
he
pyra
mid
abo
ve.T
he
slan
t h
eigh
t is
th
e h
ypot
enu
se o
f a
righ
t tr
ian
gle.
On
e le
g of
that
tri
angl
e is
th
e h
eigh
t of
th
e py
ram
id,a
nd
the
oth
er l
eg i
s h
alf
the
len
gth
of
a si
de o
f th
eba
se.U
se t
he
Pyt
hag
orea
n T
heo
rem
to
fin
d th
e sl
ant
hei
ght
�.
�2�
62�
82P
ytha
gore
an T
heor
em
�10
0S
impl
ify.
��
10Ta
ke t
he s
quar
e ro
ot o
f ea
ch s
ide.
T�
�1 2� P�
�B
Sur
face
are
a of
a p
yram
id
��1 2� (
4)(1
2)(1
0) �
122
P�
(4)(
12),
��
10,
B�
122
�38
4S
impl
ify.
Th
e su
rfac
e ar
ea i
s 38
4 sq
uar
e ce
nti
met
ers.
Fin
d t
he
surf
ace
area
of
each
reg
ula
r p
yram
id.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
547.
4 cm
261
8.0
ft2
3.4.
400
cm2
456.
8 in
2
5.6.
360
cm2
340
yd2
12 y
d
10 y
d
12 c
m13
cm
6 in
.8.
7 in
.15
in.
60�
10 c
m
45�
8 ft
15 c
m
20 c
m
late
ral e
dge
base
slan
t hei
ght
heig
ht
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Su
rfac
e A
reas
of
Pyr
amid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 12-5)
© Glencoe/McGraw-Hill A15 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Su
rfac
e A
rea
of
Pyr
amid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill68
7G
lenc
oe G
eom
etry
Lesson 12-5
Fin
d t
he
surf
ace
area
of
each
reg
ula
r p
yram
id.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
72 c
m2
646.
3 in
2
3.4.
455.
3 m
258
5.0
ft2
5.6.
99.9
mm
212
0 yd
2
7.8.
864
m2
945.
3 in
2
16 in
.
20 in
.
18 m
12 m
6 yd
7 yd
9 m
m
6 m
m
14 ft
12 ft
9 m 10
m
20 in
.
8 in
.4
cm
7 cm
©G
lenc
oe/M
cGra
w-H
ill68
8G
lenc
oe G
eom
etry
Fin
d t
he
surf
ace
area
of
each
reg
ula
r p
yram
id.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
261
yd2
147.
2 m
2
3.4.
205.
5 ft
276
.2 c
m2
5.6.
322.
2 in
278
4.7
mm
2
7.8.
75.7
yd
213
0.1
m2
9.G
AZE
BO
ST
he
roof
of
a ga
zebo
is
a re
gula
r oc
tago
nal
pyr
amid
.If
the
base
of
the
pyra
mid
has
sid
es o
f 0.
5 m
eter
s an
d th
e sl
ant
hei
ght
of t
he
roof
is
1.9
met
ers,
fin
d th
ear
ea o
f th
e ro
of.
3.8
m2
4.5
m
12 m
5.2
yd
3 yd
15 m
m
12 m
m12
in.
11 in
.
8 cm
2.5
cm
13 ft
5 ft
12 m
7 m
9 yd
10 y
d
Pra
ctic
e (
Ave
rag
e)
Su
rfac
e A
rea
of
Pyr
amid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
Answers (Lesson 12-5)
© Glencoe/McGraw-Hill A16 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csS
urf
ace
Are
as o
f P
yram
ids
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill68
9G
lenc
oe G
eom
etry
Lesson 12-5
Pre-
Act
ivit
yH
ow a
re p
yram
ids
use
d i
n a
rch
itec
ture
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-5 a
t th
e to
p of
pag
e 66
0 in
you
r te
xtbo
ok.
Why
do
you
thin
k th
at t
he a
rchi
tect
for
the
new
ent
ranc
e to
the
Lou
vre
deci
ded
to u
se a
pyr
amid
rat
her
than
a r
ecta
ngul
ar p
rism
?
Sam
ple
answ
er:T
he p
yram
id,w
ith it
s sh
arp
poin
t at
the
ver
tex
and
its s
lopi
ng s
ides
,is
mor
e un
usua
l and
dra
mat
ic t
han
are
ctan
gula
r pr
ism
.
Rea
din
g t
he
Less
on
1.In
th
e fi
gure
,AB
CD
Eh
as c
ongr
uen
t si
des
and
con
gru
ent
angl
es.
a.D
escr
ibe
this
pyr
amid
wit
h a
s sp
ecif
ic a
nam
e as
pos
sibl
e.re
gu
lar
pen
tag
on
al p
yram
id
b.
Use
th
e fi
gure
to
nam
e th
e ba
se o
f th
is p
yram
id.
AB
CD
E
c.D
escr
ibe
the
base
of
the
pyra
mid
.re
gu
lar
pen
tag
on
d.
Nam
e th
e ve
rtex
of
the
pyra
mid
.P
e.N
ame
the
late
ral f
aces
of
the
pyra
mid
.�
PAB
,�P
BC
,�P
CD
,�P
DE
,an
d �
PE
A
f.D
escr
ibe
the
late
ral
face
s.fi
ve c
on
gru
ent
iso
scel
es t
rian
gle
s
g.N
ame
the
late
ral
edge
s of
th
e py
ram
id.
P�A�
,P�B�
,P�C�
,P�D�
,an
d P�
E�h
.N
ame
the
alti
tude
of
the
pyra
mid
.P�
Q�i.
Wri
te a
n e
xpre
ssio
n f
or t
he
hei
ght
of t
he
pyra
mid
.P
Q
j.W
rite
an
exp
ress
ion
for
th
e sl
ant
hei
ght
of t
he
pyra
mid
.P
S
2.In
a r
egu
lar
squ
are
pyra
mid
,let
sre
pres
ent
the
side
len
gth
of
the
base
,hre
pres
ent
the
hei
ght,
are
pres
ent
the
apot
hem
,an
d �
repr
esen
t th
e sl
ant
hei
ght.
Als
o,le
t L
repr
esen
tth
e la
tera
l ar
ea a
nd
let
Tre
pres
ent
the
surf
ace
area
.Wh
ich
of
the
foll
owin
gre
lati
onsh
ips
are
corr
ect?
A,D
,E,F
A.
s�
2aB
.a2
��2
�h
2C
.L
�4�
s
D.h
��
�2�
a�
2 �E
.�� 2s � �2
�h
2�
�2F.
T�
s2�
2�s
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
som
eth
ing
is t
o ex
plai
n i
t to
som
eon
e el
se.S
upp
ose
that
on
e of
you
r cl
assm
ates
is
hav
ing
trou
ble
rem
embe
rin
g th
e di
ffer
ence
bet
wee
n t
he
hei
ght
and
the
slan
t h
eigh
tof
a r
egu
lar
pyra
mid
.How
can
you
exp
lain
th
is c
once
pt?
Sam
ple
an
swer
:Th
e he
ight
of
the
pyra
mid
is t
he
len
gth
of
the
per
pen
dic
ula
r se
gm
ent
fro
m t
he
vert
ex t
o t
he
cen
ter
of
the
bas
e.T
he
slan
the
ight
is t
he
len
gth
of
the
per
pen
dic
ula
r se
gm
ent
fro
m t
he
vert
ex o
f th
epy
ram
id t
o t
he
mid
po
int
of
on
e o
f th
e si
des
of
the
bas
e o
f th
e py
ram
id.
ED
CA S
B
QP
©G
lenc
oe/M
cGra
w-H
ill69
0G
lenc
oe G
eom
etry
Two
Tru
nca
ted
So
lids
To
crea
te a
tru
nca
ted
soli
d,yo
u c
ould
sta
rt w
ith
an
ord
inar
y so
lid
and
then
cu
t of
f th
eco
rner
s.A
not
her
way
to
mak
e su
ch a
sh
ape
is t
o u
se t
he
patt
ern
s on
th
is p
age.
Th
e T
run
cate
d O
ctah
edro
n
1.T
wo
copi
es o
f th
e pa
tter
n a
t th
e ri
ght
can
be
use
d to
mak
e a
tru
nca
ted
oct
ahed
ron
,a s
olid
w
ith
6 s
quar
e fa
ces
and
8 re
gula
r h
exag
onal
fa
ces.
Eac
h p
atte
rn m
akes
hal
f of
th
e tr
un
cate
doc
tah
edro
n.A
ttac
h a
djac
ent
face
s u
sin
g gl
ue
or t
ape
to m
ake
a cu
p-sh
aped
fig
ure
.
Th
e T
run
cate
d T
etra
hed
ron
2.T
he
patt
ern
bel
ow w
ill
mak
e a
tru
nca
ted
tet
rah
edro
n,
a so
lid
wit
h 8
pol
ygon
al f
aces
:4 h
exag
ons
and
4 eq
uil
ater
al t
rian
gles
.
Sol
ve.
3.F
ind
the
surf
ace
area
of
the
tru
nca
ted
octa
hed
ron
if
each
pol
ygon
in
th
e pa
tter
n h
as
side
s of
3 i
nch
es.
241.
1 in
2
4.F
ind
the
surf
ace
area
of
the
tru
nca
ted
tetr
ahed
ron
if
each
pol
ygon
in
th
e pa
tter
n h
as
side
s of
3 i
nch
es.
109.
1 in
2
Are
a F
orm
ula
s fo
r R
egu
lar
Po
lyg
on
s(s
is t
he le
ngth
of
one
side
)
tria
ngle
A�
�s 42 ��
3�
hexa
gon
A�
�3 2s2 ��
3�
octa
gon
A�
2s2 ( �
2��
1)
Tape
or
glue
her
e.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
Answers (Lesson 12-5)
© Glencoe/McGraw-Hill A17 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Su
rfac
e A
reas
of
Co
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill69
1G
lenc
oe G
eom
etry
Lesson 12-6
Late
ral A
reas
of
Co
nes
Con
es h
ave
the
foll
owin
g pr
oper
ties
.•
A c
one
has
on
e ci
rcu
lar
base
an
d on
e ve
rtex
.•
Th
e se
gmen
t w
hos
e en
dpoi
nts
are
th
e ve
rtex
an
d th
e ce
nte
r of
th
e ba
se i
s th
e ax
isof
th
e co
ne.
•T
he
segm
ent
that
has
on
e en
dpoi
nt
at t
he
vert
ex,i
s pe
rpen
dicu
lar
to t
he
base
,an
d h
as i
ts o
ther
en
dpoi
nt
on t
he
base
is
the
alti
tud
eof
th
e co
ne.
•F
or a
rig
ht
con
eth
e ax
is i
s al
so t
he
alti
tude
,an
d an
y se
gmen
t fr
om t
he
circ
um
fere
nce
of
th
e ba
se t
o th
e ve
rtex
is
the
slan
t h
eigh
t�.
If a
con
e is
not
a r
igh
t co
ne,
it i
s ob
liqu
e.
Lat
eral
Are
a If
a co
ne h
as a
late
ral a
rea
of L
squa
re u
nits
, a
slan
t he
ight
of
�un
its,
of
a C
on
ean
d th
e ra
dius
of
the
base
is r
units
, th
en L
��
r�.
Fin
d t
he
late
ral
area
of
a co
ne
wit
h s
lan
t h
eigh
t of
10
cen
tim
eter
s an
d a
bas
e w
ith
a r
adiu
s of
6 c
enti
met
ers.
L�
�r �
Late
ral a
rea
of a
con
e
��
(6)(
10)
r�
6, �
�10
�18
8.5
Sim
plify
.
Th
e la
tera
l ar
ea i
s ab
out
188.
5 sq
uar
e ce
nti
met
ers.
Fin
d l
ater
al a
rea
of e
ach
cir
cula
r co
ne.
Rou
nd
to
the
nea
rest
ten
th.
1.2.
47.1
cm
242
4.1
cm2
3.4.
391.
8 m
281
6.8
mm
2
5.6.
204.
2 in
228
4.3
yd2
8 yd
16 y
d12
in.
5 in
.
26 m
m
20 m
m
6��3
m
60�
9 cm
15 c
m
3 cm
4 cm
6 cm
10 c
m
axis
base
base
�sl
ant h
eigh
t
right
con
eob
lique
con
e
altit
ude
VV
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill69
2G
lenc
oe G
eom
etry
Surf
ace
Are
as o
f C
on
esT
he
surf
ace
area
of
a co
ne
is t
he
late
ral
area
of
the
con
e pl
us
the
area
of
the
base
.
Su
rfac
e A
rea
If a
cone
has
a s
urfa
ce a
rea
of T
squa
re u
nits
, a
slan
t he
ight
of
of
a R
igh
t C
on
e�
units
, an
d th
e ra
dius
of
the
base
is r
units
, th
en T
��
r��
�r2
.
For
th
e co
ne
abov
e,fi
nd
th
e su
rfac
e ar
ea t
o th
e n
eare
st t
enth
if
the
rad
ius
is 6
cen
tim
eter
s an
d t
he
hei
ght
is 8
cen
tim
eter
s.T
he
slan
t h
eigh
t is
th
e h
ypot
enu
se o
f a
righ
t tr
ian
gle
wit
h l
egs
of l
engt
h 6
an
d 8.
Use
th
eP
yth
agor
ean
Th
eore
m.
�2�
62�
82P
ytha
gore
an T
heor
em
�2�
100
Sim
plify
.
��
10Ta
ke t
he s
quar
e ro
ot o
f ea
ch s
ide.
T�
�r�
��
r2S
urfa
ce a
rea
of a
con
e
��
(6)(
10)
��
�62
r�
6, �
�10
�30
1.6
Sim
plify
.
Th
e su
rfac
e ar
ea i
s ab
out
301.
6 sq
uar
e ce
nti
met
ers.
Fin
d t
he
surf
ace
area
of
each
con
e.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
678.
6 cm
223
5.6
ft2
3.4.
282.
7 cm
212
1.4
in2
5.6.
2890
.3 m
260
3.2
yd260�
8��3
yd26
m
40 m
4 in
.
45�
12 c
m
13 c
m
5 ft
30�
9 cm
12 c
m
�sl
ant h
eigh
t
heig
ht
r
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Su
rfac
e A
reas
of
Co
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 12-6)
© Glencoe/McGraw-Hill A18 Glencoe Geometry
Skil
ls P
ract
ice
Su
rfac
e A
reas
of
Co
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill69
3G
lenc
oe G
eom
etry
Lesson 12-6
Fin
d t
he
surf
ace
area
of
each
con
e.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
298.
5 m
211
60.1
ft2
3.4.
728.
8 in
273
5.1
mm
2
5.6.
661.
6 cm
214
0.9
yd2
7.F
ind
the
surf
ace
area
of
a co
ne i
f th
e he
ight
is
12 i
nche
s an
d th
e sl
ant
heig
ht i
s 15
inc
hes.
678.
6 in
2
8.F
ind
the
surf
ace
area
of
a co
ne
if t
he
hei
ght
is 9
cen
tim
eter
s an
d th
e sl
ant
hei
ght
is
12 c
enti
met
ers.
497.
1 cm
2
9.F
ind
the
surf
ace
area
of
a co
ne if
the
hei
ght
is 1
0 m
eter
s an
d th
e sl
ant
heig
ht is
14
met
ers.
732.
5 m
2
10.F
ind
the
surf
ace
area
of
a co
ne
if t
he
hei
ght
is 5
fee
t an
d th
e sl
ant
hei
ght
is 7
fee
t.
183.
1 ft
2
4 yd
6 yd
7 cm
22 c
m
17 m
m9 m
m
8 in
.
21 in
.
10 ft
25 ft
14 m
5 m
©G
lenc
oe/M
cGra
w-H
ill69
4G
lenc
oe G
eom
etry
Fin
d t
he
surf
ace
area
of
each
con
e.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
622.
0 in
257
8.7
mm
2
3.4.
5733
.4 y
d2
207.
3 ft
2
5.6.
130.
7 m
264
0.7
cm2
7.F
ind
the
surf
ace
area
of
a co
ne
if t
he
hei
ght
is 8
fee
t an
d th
e sl
ant
hei
ght
is 1
0 fe
et.
301.
6 ft
2
8.F
ind
the
surf
ace
area
of
a co
ne
if t
he
hei
ght
is 1
4 ce
nti
met
ers
and
the
slan
t h
eigh
t is
16.4
cen
tim
eter
s.
669.
3 cm
2
9.F
ind
the
surf
ace
area
of
a co
ne
if t
he
hei
ght
is 1
2 in
ches
an
d th
e di
amet
er i
s 27
in
ches
.
1338
.6 in
2
10.H
ATS
Cuo
ng b
ough
t a
coni
cal
hat
on a
rec
ent
trip
to
cent
ral V
ietn
am.T
he b
asic
fra
me
ofth
e h
at i
s 16
hoo
ps o
f ba
mbo
o th
at g
radu
ally
dim
inis
h i
n s
ize.
Th
e h
at i
s co
vere
d in
pal
mle
aves
.If
the
hat
has
a d
iam
eter
of
50 c
enti
met
ers
and
a sl
ant
hei
ght
of 3
2 ce
nti
met
ers,
wh
at i
s th
e la
tera
l ar
ea o
f th
e co
nic
al h
at?
abo
ut
2513
.3 c
m2
7 cm
21 c
m5
m4
m
3 ft
19 ft
48 y
d25 y
d
7 m
m18
mm
9 in
.13
in.
Pra
ctic
e (
Ave
rag
e)
Su
rfac
e A
reas
of
Co
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
Answers (Lesson 12-6)
© Glencoe/McGraw-Hill A19 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
urf
ace
Are
as o
f C
on
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill69
5G
lenc
oe G
eom
etry
Lesson 12-6
Pre-
Act
ivit
yH
ow i
s th
e la
tera
l ar
ea o
f a
con
e u
sed
to
cove
r te
pee
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-6 a
t th
e to
p of
pag
e 66
6 in
you
r te
xtbo
ok.
If y
ou w
ante
d to
bu
ild
a te
pee
of a
cer
tain
siz
e,h
ow w
ould
it
hel
p yo
u t
okn
ow t
he
form
ula
for
th
e la
tera
l ar
ea o
f a
con
e?S
amp
le a
nsw
er:T
he
form
ula
wo
uld
hel
p y
ou
est
imat
e h
ow
man
y an
imal
ski
ns
you
wo
uld
nee
d f
or
the
tep
ee.
Rea
din
g t
he
Less
on
1.
a.W
hic
h n
et w
ill
give
th
e co
ne
wit
h t
he
grea
test
lat
eral
are
a?N
et B
b.
Wh
ich
net
wil
l gi
ve t
he
tall
est
con
e?N
et C
2.R
efer
to
the
figu
re a
t th
e ri
ght.
Su
ppos
e yo
u h
ave
rem
oved
th
e ci
rcu
lar
base
of
the
con
e an
d cu
t fr
om V
to A
so t
hat
you
can
un
roll
th
e la
tera
lsu
rfac
e on
to a
fla
t ta
ble.
a.H
ow c
an y
ou b
e su
re t
hat
th
e fl
atte
ned
-ou
t pi
ece
is a
sec
tor
of a
cir
cle?
Sam
ple
an
swer
:B
efo
re y
ou
un
roll
the
late
ral s
urf
ace,
all
po
ints
on
th
e b
ott
om
rim
of
the
con
e ar
e �
un
its
fro
m V
.A
fter
yo
u f
latt
en o
ut
the
surf
ace,
tho
se p
oin
ts a
re s
till
�u
nit
s fr
om
V.T
his
mea
ns
that
th
ey w
ill li
e o
n a
cir
cle
wit
h
cen
ter
Van
d r
adiu
s �.
b.
How
do
you
kn
ow t
hat
th
e fl
atte
ned
-ou
t pi
ece
is n
ot a
fu
ll c
ircl
e?S
amp
le a
nsw
er:
r�
�
3.S
upp
ose
you
hav
e a
righ
t co
ne
wit
h r
adiu
s r,
diam
eter
d,h
eigh
t h
,an
d sl
ant
hei
ght
�.W
hic
h o
f th
e fo
llow
ing
rela
tion
ship
s in
volv
ing
thes
e le
ngt
hs
are
corr
ect?
C,E
A.
r�
2dB
.r�
h�
�C
.r2
�h
2�
�2
D.r
2�
�2�
h2
E.
r�
��2
�h
�2 �
F.h
��
��2
�r
�2 �
Hel
pin
g Y
ou
Rem
emb
er
4.O
ne
way
to
rem
embe
r a
new
for
mu
la i
s to
rel
ate
it t
o a
form
ula
you
alr
eady
kn
ow.
Exp
lain
how
th
e fo
rmu
las
for
the
late
ral
area
s of
a p
yram
id a
nd
a co
ne
are
sim
ilar
.S
amp
le a
nsw
er:
Bo
th f
orm
ula
s sa
y th
at t
he
late
ral a
rea
incl
ud
es t
he
dis
tan
ce a
rou
nd
th
e b
ase
mu
ltip
lied
by
the
slan
t h
eig
ht.
V
PA
B
h r
�
Net
AN
et B
Net
C
©G
lenc
oe/M
cGra
w-H
ill69
6G
lenc
oe G
eom
etry
Co
ne
Pat
tern
s
Th
e p
atte
rn a
t th
e ri
ght
is m
ade
from
a
circ
le.I
t ca
n b
e fo
lded
to
mak
e a
con
e.
1.M
easu
re t
he
radi
us
of t
he
circ
le t
o th
e n
eare
st c
enti
met
er. 4
cm
2.T
he
patt
ern
is
wh
at f
ract
ion
of
the
com
plet
e ci
rcle
? �3 4�
3.W
hat
is
the
circ
um
fere
nce
of
the
com
plet
e ci
rcle
? 8�
cm
4.H
ow l
ong
is t
he
circ
ula
r ar
c th
at i
s th
e ou
tsid
e of
th
e pa
tter
n?
6�cm
5.C
ut
out
the
patt
ern
an
d ta
pe i
t to
geth
er t
o fo
rm a
con
e.S
ee s
tud
ents
’wo
rk.
6.M
easu
re t
he
diam
eter
of
the
circ
ula
r ba
se o
f th
e co
ne.
6 cm
7.W
hat
is
the
circ
um
fere
nce
of
the
base
of
the
con
e? 6
�cm
8.W
hat
is
the
slan
t h
eigh
t of
th
e co
ne?
4 c
m
9.U
se t
he
Pyt
hag
orea
n T
heo
rem
to
calc
ula
te t
he
hei
ght
of t
he
con
e.U
se a
dec
imal
app
roxi
mat
ion
.Ch
eck
you
r ca
lcu
lati
on b
y m
easu
rin
g th
e h
eigh
t w
ith
a m
etri
c ru
ler.
2.65
cm
10.F
ind
the
late
ral
area
.12�
cm2
11.F
ind
the
tota
l su
rfac
e ar
ea.2
1�cm
2
Mak
e a
pap
er p
atte
rn f
or e
ach
con
e w
ith
th
e gi
ven
mea
sure
men
ts.
Th
en c
ut
the
pat
tern
ou
t an
d m
ake
the
con
e.F
ind
th
e m
easu
rem
ents
.
12.
13.
diam
eter
of
base
�8
cmdi
amet
er o
f ba
se �
10 c
m
late
ral
area
�24
�cm
2la
tera
l ar
ea �
50�
cm2
hei
ght
of c
one
�4.
5 cm
hei
ght
of c
one
�8.
7 cm
(to
nea
rest
ten
th o
f a
cen
tim
eter
)(t
o n
eare
st t
enth
of
a ce
nti
met
er)
20 c
m12
0�6
cm
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
Answers (Lesson 12-6)
© Glencoe/McGraw-Hill A20 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Su
rfac
e A
reas
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill69
7G
lenc
oe G
eom
etry
Lesson 12-7
Pro
per
ties
of
Sph
eres
A s
ph
ere
is t
he
locu
s of
all
poi
nts
th
at
are
a gi
ven
dis
tan
ce f
rom
a g
iven
poi
nt
call
ed i
ts c
ente
r.
Her
e ar
e so
me
term
s as
soci
ated
wit
h a
sph
ere.
•A
rad
ius
is a
seg
men
t w
hos
e en
dpoi
nts
are
th
e ce
nte
r of
th
e sp
her
e an
d a
poin
t on
th
e sp
her
e.•
A c
hor
dis
a s
egm
ent
wh
ose
endp
oin
ts a
re p
oin
ts
on t
he
sph
ere.
•A
dia
met
eris
a c
hor
d th
at c
onta
ins
the
sph
ere’
s ce
nte
r.•
A t
ange
nt
is a
lin
e th
at i
nte
rsec
ts t
he
sph
ere
in
exac
tly
one
poin
t.•
A g
reat
cir
cle
is t
he
inte
rsec
tion
of
a sp
her
e an
d a
plan
e th
at c
onta
ins
the
cen
ter
of t
he
sph
ere.
•A
hem
isp
her
eis
on
e-h
alf
of a
sph
ere.
Eac
h g
reat
ci
rcle
of
a sp
her
e de
term
ines
tw
o h
emis
pher
es.
Det
erm
ine
the
shap
es y
ou g
et w
hen
you
in
ters
ect
a p
lan
e w
ith
a s
ph
ere.
The
inte
rsec
tion
of p
lane
MT
he in
ters
ectio
n of
pla
ne N
The
inte
rsec
tion
of p
lane
Pan
d sp
here
Ois
poi
nt P
.an
d sp
here
Ois
circ
le Q
.an
d sp
here
Ois
circ
le O
.
A p
lan
e ca
n i
nte
rsec
t a
sph
ere
in a
poi
nt,
in a
cir
cle,
or i
n a
gre
at c
ircl
e.
Des
crib
e ea
ch o
bje
ct a
s a
mod
el o
f a
circ
le,a
sp
her
e,a
hem
isp
her
e,or
non
e of
th
ese.
1.a
base
ball
2.a
pan
cake
3.th
e E
arth
sph
ere
circ
lesp
her
e
4.a
kett
le g
rill
cov
er5.
a ba
sket
ball
rim
6.co
la c
an
hem
isp
her
eci
rcle
no
ne
of
thes
e
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
is t
rue
or f
als
e.
7.A
ll l
ines
in
ters
ecti
ng
a sp
her
e ar
e ta
nge
nt
to t
he
sph
ere.
fals
e
8.E
very
pla
ne
that
in
ters
ects
a s
pher
e m
akes
a g
reat
cir
cle.
fals
e
9.T
he
east
ern
hem
isph
ere
of E
arth
is
con
gru
ent
to t
he
wes
tern
hem
isph
ere.
tru
e
10.T
he
diam
eter
of
a sp
her
e is
con
gru
ent
to t
he
diam
eter
of
a gr
eat
circ
le.
tru
e
OP
O QN
O PM
R�S�
is a
rad
ius.
A�B�
is a
cho
rd.
S�T�
is a
dia
met
er.V
X��
�is
a t
ange
nt.
The
circ
le th
at c
onta
ins
poin
ts S
, M, T
, and
Nis
a gr
eat c
ircle
; it d
eter
min
es tw
o he
mis
pher
es.
chor
dta
ngen
t
grea
t circ
le
diam
eter
radi
usS
T
W
RN
B
V
X
A
M
sphe
re
cent
er
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill69
8G
lenc
oe G
eom
etry
Surf
ace
Are
as o
f Sp
her
esYo
u c
an t
hin
k of
th
e su
rfac
e ar
ea o
f a
sph
ere
as t
he
tota
l ar
ea o
f al
l of
th
e n
onov
erla
ppin
g st
rips
it
wou
ld t
ake
to c
over
th
esp
her
e.If
ris
th
e ra
diu
s of
th
e sp
her
e,th
en t
he
area
of
a gr
eat
circ
le o
f th
esp
her
e is
�r2
.Th
e to
tal
surf
ace
area
of
the
sph
ere
is f
our
tim
es t
he
area
of
agr
eat
circ
le.
Su
rfac
e A
rea
of
a S
ph
ere
If a
sphe
re h
as a
sur
face
are
a of
Tsq
uare
uni
ts a
nd a
rad
ius
of r
units
, th
en T
�4�
r2.
Fin
d t
he
surf
ace
area
of
a sp
her
e to
th
e n
eare
st t
enth
if
th
e ra
diu
s of
th
e sp
her
e is
6 c
enti
met
ers.
T�
4�r2
Sur
face
are
a of
a s
pher
e
�4�
�62
r�
6
�45
2.4
Sim
plify
.
Th
e su
rfac
e ar
ea i
s 45
2.4
squ
are
cen
tim
eter
s.
Fin
d t
he
surf
ace
area
of
each
sp
her
e w
ith
th
e gi
ven
rad
ius
or d
iam
eter
to
the
nea
rest
ten
th.
1.r
�8
cm2.
r�
2 �2�
ft
804.
2 cm
210
0.5
ft2
3.r
��
cm4.
d�
10 i
n.
124.
0 cm
231
4.2
in2
5.d
�6�
m6.
d�
16 y
d
1116
.2 m
280
4.2
yd2
7.F
ind
the
surf
ace
area
of
a h
emis
pher
e w
ith
rad
ius
12 c
enti
met
ers.
1357
.2 c
m2
8.F
ind
the
surf
ace
area
of
a h
emis
pher
e w
ith
dia
met
er �
cen
tim
eter
s.
23.3
cm
2
9.F
ind
the
radi
us
of a
sph
ere
if t
he
surf
ace
area
of
a h
emis
pher
e is
19
2�sq
uar
e ce
nti
met
ers.
8 cm
6 cmr
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Su
rfac
e A
reas
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 12-7)
© Glencoe/McGraw-Hill A21 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Su
rfac
e A
reas
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill69
9G
lenc
oe G
eom
etry
Lesson 12-7
In t
he
figu
re,A
is t
he
cen
ter
of t
he
sph
ere,
and
pla
ne
Tin
ters
ects
th
e sp
her
e in
cir
cle
E.R
oun
d t
o th
e n
eare
stte
nth
if
nec
essa
ry.
1.If
AE
�5
and
DE
�12
,fin
d A
D.
13
2.If
AE
�7
and
DE
�15
,fin
d A
D.
16.6
3.If
th
e ra
diu
s of
th
e sp
her
e is
18
un
its
and
the
radi
us
of �
Eis
17
un
its,
fin
d A
E.
5.9
4.If
th
e ra
diu
s of
th
e sp
her
e is
10
un
its
and
the
radi
us
of �
Eis
9 u
nit
s,fi
nd
AE
.
4.4
5.If
Mis
a p
oin
t on
�E
and
AD
�23
,fin
d A
M.
23
Fin
d t
he
surf
ace
area
of
each
sp
her
e or
hem
isp
her
e.R
oun
d t
o th
e n
eare
st t
enth
.
6.7.
615.
8 in
232
17.0
m2
8.a
hem
isph
ere
wit
h a
rad
ius
of t
he
grea
t ci
rcle
8 y
ards
603.
2 yd
2
9.a
hem
isph
ere
wit
h a
rad
ius
of t
he
grea
t ci
rcle
2.5
mil
lim
eter
s
58.9
mm
2
10.a
sph
ere
wit
h t
he
area
of
a gr
eat
circ
le 2
8.6
inch
es
114.
4 in
2
32 m
7 in
.
A ED
T
©G
lenc
oe/M
cGra
w-H
ill70
0G
lenc
oe G
eom
etry
In t
he
figu
re,C
is t
he
cen
ter
of t
he
sph
ere,
and
pla
ne
Bin
ters
ects
th
e sp
her
e in
cir
cle
R.R
oun
d t
o th
e n
eare
stte
nth
if
nec
essa
ry.
1.If
CR
�4
and
SR
�14
,fin
d C
S.
14.6
2.If
CR
�7
and
SR
�24
,fin
d C
S.
25
3.If
th
e ra
diu
s of
th
e sp
her
e is
28
un
its
and
the
radi
us
of �
Ris
26
un
its,
fin
d C
R.
10.4
4.If
Jis
a p
oin
t on
�R
and
CS
�7.
3,fi
nd
CJ
.
7.3
Fin
d t
he
surf
ace
area
of
each
sp
her
e or
hem
isp
her
e.R
oun
d t
o th
e n
eare
st t
enth
.
5.6.
530.
9 cm
224
,884
.6 f
t2
7.a
sph
ere
wit
h t
he
area
of
a gr
eat
circ
le 2
9.8
met
ers
119.
2 m
2
8.a
hem
isph
ere
wit
h a
rad
ius
of t
he
grea
t ci
rcle
8.4
in
ches
665.
0 in
2
9.a
hem
isph
ere
wit
h t
he
circ
um
fere
nce
of
a gr
eat
circ
le 1
8 m
illi
met
ers
77.3
mm
2
10.S
POR
TSA
sta
nda
rd s
ize
5 so
ccer
bal
l fo
r ag
es 1
3 an
d ol
der
has
a c
ircu
mfe
ren
ce o
f27
–28
inch
es.S
upp
ose
Bre
ck i
s on
a t
eam
th
at p
lays
wit
h a
28-
inch
soc
cer
ball
.Fin
d th
esu
rfac
e ar
ea o
f th
e ba
ll.
abo
ut
249.
6 in
2
89 ft
6.5
cm
C RS
B
Pra
ctic
e (
Ave
rag
e)
Su
rfac
e A
reas
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
Answers (Lesson 12-7)
© Glencoe/McGraw-Hill A22 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csS
urf
ace
Are
as o
f S
ph
eres
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill70
1G
lenc
oe G
eom
etry
Lesson 12-7
Pre-
Act
ivit
yH
ow d
o m
anu
fact
ure
rs o
f sp
orts
eq
uip
men
t u
se t
he
surf
ace
area
s of
sp
her
es?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-7 a
t th
e to
p of
pag
e 67
1 in
you
r te
xtbo
ok.
How
wou
ld k
now
ing
the
form
ula
for
th
e su
rfac
e ar
ea o
f a
sph
ere
hel
pm
anu
fact
ure
rs o
f be
ach
bal
ls?
Sam
ple
an
swer
:Th
e su
rfac
e ar
ea o
fth
e b
all t
ells
th
e m
anu
fact
ure
r h
ow
mu
ch m
ater
ial i
s n
eed
ed t
om
ake
each
bal
l.
Rea
din
g t
he
Less
on
1.In
th
e fi
gure
,Pis
th
e ce
nte
r of
th
e sp
her
e.N
ame
each
of
the
foll
owin
g in
th
e fi
gure
.
a.th
ree
radi
i of
th
e sp
her
eP�
T�,P�
R�,a
nd
P�S�
b.
a di
amet
er o
f th
e sp
her
eR�
S�c.
two
chor
ds o
f th
e sp
her
eR�
S�an
d U�
V�d
.a
grea
t ci
rcle
of
the
sph
ere
�P
e.a
tan
gen
t to
th
e sp
her
eW
Y��
�
f.th
e po
int
of t
ange
ncy
X
2.D
eter
min
e w
het
her
eac
h s
ente
nce
is
som
etim
es,a
lway
s,or
nev
ertr
ue.
a.If
a s
pher
e an
d a
plan
e in
ters
ect
in m
ore
than
on
e po
int,
thei
r in
ters
ecti
on w
ill
be a
grea
t ci
rcle
.so
met
imes
b.
A g
reat
cir
cle
has
th
e sa
me
cen
ter
as t
he
sph
ere.
alw
ays
c.T
he
endp
oin
ts o
f a
radi
us
of a
sph
ere
are
two
poin
ts o
n t
he
sph
ere.
nev
erd
.A
ch
ord
of a
sph
ere
is a
dia
met
er o
f th
e sp
her
e.so
met
imes
e.A
rad
ius
of a
gre
at c
ircl
e is
als
o a
radi
us
of t
he
sph
ere.
alw
ays
3.M
atch
eac
h s
urf
ace
area
for
mu
la w
ith
th
e n
ame
of t
he
appr
opri
ate
soli
d.
a.T
��
r��
�r2
vii.
regu
lar
pyra
mid
b.
T�
Ph
�2B
ivii
.hem
isph
ere
c.T
�4�
r2v
iii.
cyli
nde
r
d.
T�
�1 2� P�
�B
iiv
.pr
ism
e.T
�2�
rh�
2�r2
iiiv.
sph
ere
f.T
�3�
r2ii
vi.c
one
Hel
pin
g Y
ou
Rem
emb
er4.
Man
y st
ude
nts
hav
e tr
oubl
e re
mem
beri
ng
all
of t
he
form
ula
s th
ey h
ave
lear
ned
in
th
isch
apte
r.W
hat
is
an e
asy
way
to
rem
embe
r th
e fo
rmu
la f
or t
he
surf
ace
area
of
a sp
her
e?S
amp
le a
nsw
er:
A s
ph
ere
do
esn
’t h
ave
any
late
ral f
aces
or
bas
es,s
o t
he
exp
ress
ion
in t
he
form
ula
fo
r it
s su
rfac
e ar
ea h
as ju
st o
ne
term
,4�
r2,
rath
er t
han
bei
ng
th
e su
m o
f th
e ex
pre
ssio
ns
for
the
late
ral a
rea
and
th
ear
ea o
f th
e b
ases
like
th
e o
ther
s.
RS
T
P
W
V
XY
U
©G
lenc
oe/M
cGra
w-H
ill70
2G
lenc
oe G
eom
etry
Do
ubl
ing
Siz
esC
onsi
der
wh
at h
appe
ns
to s
urf
ace
area
wh
en t
he
side
s of
a f
igu
re a
re d
oubl
ed.
Th
e si
des
of t
he
larg
e cu
be a
re t
wic
e th
e si
ze o
f th
e si
des
of t
he
smal
l cu
be.
1.H
ow l
ong
are
the
edge
s of
th
e la
rge
cube
?6
in.
2.W
hat
is
the
surf
ace
area
of
the
smal
l cu
be?
54 in
2
3.W
hat
is
the
surf
ace
area
of
the
larg
e cu
be?
216
in2
4.T
he
surf
ace
area
of
the
larg
e cu
be i
s h
ow m
any
tim
es g
reat
er
than
th
at o
f th
e sm
all
cube
?4
tim
es
Th
e ra
diu
s of
th
e la
rge
sph
ere
at t
he
righ
t is
tw
ice
the
radi
us
of
the
smal
l sp
her
e.
5.W
hat
is
the
surf
ace
area
of
the
smal
l sp
her
e?40
0� m
2
6.W
hat
is
the
surf
ace
area
of
the
larg
e sp
her
e? 1
600�
m2
7.T
he
surf
ace
area
of
the
larg
e sp
her
e is
how
man
y ti
mes
gr
eate
r th
an t
he
surf
ace
area
of
the
smal
l sp
her
e?4
tim
es
8.It
app
ears
th
at i
f th
e di
men
sion
s of
a s
olid
are
dou
bled
,th
e su
rfac
e ar
ea i
s m
ult
ipli
ed b
y ��
����
���.
4
Now
con
side
r h
ow d
oubl
ing
the
dim
ensi
ons
affe
cts
the
volu
me
of a
cu
be.
Th
e si
des
of t
he
larg
e cu
be a
re t
wic
e th
e si
ze o
f th
e sm
all
cube
.
9.H
ow l
ong
are
the
edge
s of
th
e la
rge
cube
?10
in.
10.W
hat
is
the
volu
me
of t
he
smal
l cu
be?
125
in3
11.W
hat
is
the
volu
me
of t
he
larg
e cu
be?
1000
in3
12.T
he
volu
me
of t
he
larg
e cu
be i
s h
ow m
any
tim
es g
reat
er t
han
th
at o
f th
e sm
all
cube
?8
tim
es
Th
e la
rge
sph
ere
at t
he
righ
t h
as t
wic
e th
e ra
diu
s of
th
e sm
all
sph
ere.
13.W
hat
is
the
volu
me
of t
he
smal
l sp
her
e?36
� m
3
14.W
hat
is
the
volu
me
of t
he
larg
e sp
her
e?28
8� m
3
15.T
he
volu
me
of t
he
larg
e sp
her
e is
how
man
y ti
mes
gre
ater
th
an t
he
volu
me
of t
he
smal
l sp
her
e?8
tim
es
16.I
t ap
pear
s th
at i
f th
e di
men
sion
s of
a s
olid
are
dou
bled
,th
e vo
lum
e is
mu
ltip
lied
by
����
����
�.8
3 m
5 in
.
3 m
5 in
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
Answers (Lesson 12-7)
© Glencoe/McGraw-Hill A23 Glencoe Geometry
Chapter 12 Assessment Answer Key Form 1 Form 2APage 703 Page 704 Page 705
(continued on the next page)
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
C
A
B
D
B
D
B
D
C
D
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
C
A
B
A
B
C
C
B
D
A
1020 ft2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
D
C
D
C
A
C
B
B
C
D
© Glencoe/McGraw-Hill A24 Glencoe Geometry
Chapter 12 Assessment Answer KeyForm 2A (continued) Form 2BPage 706 Page 707 Page 708
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
A
C
D
A
B
B
C
B
A
A
391.6 ft2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
D
A
B
D
C
B
B
D
B
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
C
A
C
C
D
A
B
B
D
C
53 ft2
© Glencoe/McGraw-Hill A25 Glencoe Geometry
Chapter 12 Assessment Answer KeyForm 2CPage 709 Page 710
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
�PQRS, �PQT,�QTR, �RTS, �PTS
hexagonal pyramid
12
Sample answer:
240 in2
120 cm2
3536 units2
7.2 in2
7 gal
6 6
5 4 44
4
5
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
524.1 yd2
6 in.
270 in2
270 � 150�3� in2
144 units2
54.5 cm
62.8 ft2
113.1 ft2
17 m
235.6 cm2
38.5 in2
© Glencoe/McGraw-Hill A26 Glencoe Geometry
Chapter 12 Assessment Answer KeyForm 2DPage 711 Page 712
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
G�J�, H�J�, I�J�, G�H�,
H�I�, G�I�
pentagonalprism
12
Sample answer:
840 cm2
750 in2
258 ft2
3 gal
180 in2
88
8 8
88
6
66
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
845.2 m2
7 ft
540 ft2
931.0 ft2
156.9 units2
22.4 ft
204.2 cm2
282.7 cm2
5 m
1140.4 in2
113.1 in2
© Glencoe/McGraw-Hill A27 Glencoe Geometry
Chapter 12 Assessment Answer KeyForm 3Page 713 Page 714
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
�XYZ, �UVW
octahedron
20
Sample answer:
128 � 4�21�units2
35 � 7�13� ft2
528 units2
17,837.8 ft2
32,435.2 ft2
It is multiplied by 4.
52
2
2
22
2
2
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
468 in2
842.1 in2
It is multiplied by 9.
233.8 in2
387.7 in2
182.0 cm2
2�21�
3�r2
1709 ft2
700 ft2
© Glencoe/McGraw-Hill A28 Glencoe Geometry
Chapter 12 Assessment Answer KeyPage 715, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts ofpyramids, prisms, cylinders, cones, spheres, surface area,lateral area, nets, and properties of solid figures.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Figures and drawings are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of pyramids,prisms, cylinders, cones, spheres, surface area, lateralarea, nets, and properties of solid figures.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Figures and drawings are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts ofpyramids, prisms, cylinders, cones, spheres, surface area,lateral area, nets, and properties of solid figures.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Figures and drawings are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work shown to substantiate the
final computation.• Figures and drawings may be accurate but lack detail or
explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the conceptsof pyramids, prisms, cylinders, cones, spheres, surfacearea, lateral area, nets, and properties of solid figures.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Figures and drawings are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
© Glencoe/McGraw-Hill A29 Glencoe Geometry
An
swer
s
Chapter 12 Assessment Answer KeyPage 715, Open-Ended Assessment
Sample Answers
1. a.
b. e � f � v � 2
2. The lateral area is the area of the lateral faces. The surface area includesthe area of the lateral faces plus the areas of the two bases.
3. a.
b. �ABCD
c. �ABE, �BCE, �CDE, �ADE
d.
4.
5. a.
b. 38� in2
6. Sample answer: Sam is painting the walls of a room. The room is 12 feetlong, 10 feet wide, and 8 feet high. A gallon of paint covers 400 square feetand costs $16 per gallon. Find the cost to paint the room.
2 in. 6 in.3 in.
Oblique Right
A D
CB
E
Figure No. of Edges (e) No. of Faces (f ) No. of Vertices (v ) f � v
Triangular Pyramid 6 4 4 8
Triangular Prism 9 5 6 11
Cube 12 6 8 14
Square Pyramid 8 5 5 10
Hexagonal Prism 18 8 12 20
Hexagonal Pyramid 12 7 7 14
In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A30 Glencoe Geometry
Chapter 12 Assessment Answer KeyVocabulary Test/Review Quiz 1 Quiz 3Page 716 Page 717 Page 718
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
slant height
cone
sphere
perspective view
Platonic Solids
prism
pyramid
surface area
right cylinder
hemisphere
the sum of the areasof the lateral faces
a prism whoselateral edges are
also altitudes
the intersection of asphere and a plane
containing thecenter of the sphere
Quiz 2Page 717
Quiz 4Page 718
1.
2.
3.
4.
Sample answer:
Sample answer:
D
1022
22
2
22 22
2
2222
2
1.
2.
3.
4.
5.
2 in.
12 units
rectangle
3870.4 units2
4630.7 units2
1.
2.
3.
4.
5.
81 units2
116.1 units2
260 cm2
188.5 ft2
267.0 ft2
1.
2.
3.
4.
5.
B�C�
AH���
�D
4071.5 in2
It is multiplied by 4.
© Glencoe/McGraw-Hill A31 Glencoe Geometry
Chapter 12 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 719 Page 720
An
swer
s
Part I
Part II
6.
7.
8.
9.
10.
Sample answer:
1656 units2
92.8 units2
282.7 in2
6
5
5
4
4
4 53
1.
2.
3.
4.
5.
C
A
D
A
D
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
�AFD and �BFC
false
It alternates
between �12
� and 2.
m�X � 63,m�Z � 44,y � 34 cm
27.6 in. and 23.1 in.
magnitude: 11.7,direction: 149.0°
circle
28
80 cm2; 48 cm
14.5 m
5.0 in.
© Glencoe/McGraw-Hill A32 Glencoe Geometry
Chapter 12 Assessment Answer KeyStandardized Test Practice
Page 721 Page 722
1.
2.
3.
4.
5.
6.
7.
8. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D 9. 10.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
11.
12.
13.
14.
15.
16.
2.6 m
25
51.4 cm2
pentagonalpyramid
3141.6 in2
2206.2 cm2
1 4 5