Honors Geometry 22/23 February 2012Warm Up1. A tall fir tree casts a shadow that measures 8 ½

yards at the same time a six foot man casts a 2 ½ foot shadow. What is the height of the fir tree?

a) 20.4 ft b) 61.2 ft c) 63.75 ft d) 153 ftShow your work and explain how you know you are

correct.

2. Find r if C = a) 8.5 in b) 11 in

ObjectiveStudents will find surface area and volume of various

figures.

Students will take notes, participate in class discussion and use think-pair-share.

due TODAYdue TODAYHW grade: TEST CORRECTIONSHW grade: TEST CORRECTIONS

FORMAT:FORMAT:1) Explain what you did incorrectly1) Explain what you did incorrectly

2) rework the problem correctly2) rework the problem correctlyshowing all stepsshowing all steps

3) ATTACH corrections to test paper3) ATTACH corrections to test paper

DO pg. 533: 1, 7, 12DO pg. 533: 1, 7, 12Due February 24Due February 24

Worksheet SA of Cylinders and ConesWorksheet SA of Cylinders and Cones# 1- 6, 9, 10, 12, 13- # 1- 6, 9, 10, 12, 13- show work on separate papershow work on separate paper

VOLUME and SA

BASICALLY,

SA = AREASA = AREAbase(s)base(s) + LSA + LSA (add the areas of the faces)

VVPRISM/CYLINDERPRISM/CYLINDER = A = ABASEBASE x HEIGHT x HEIGHT

HEIGHT is ALWAYS PERPENDICULAR distance

Which has more volume?more surface area?

You can make two different cylinders by rolling a piece of notebook paper either “longways or shortways”. WHICH SHAPE HAS MORE VOLUME?WHICH SHAPE HAS MORE Surface Area? (including the bases?) Can you explain why?

Geometric SolidsGeometric Solids 2 Bases2 Bases 1 Base1 Base No BaseNo Base

Prisms & Prisms & CylindersCylinders Cones & Cones &

pyramidspyramidsSpheresSpheres

Bases are congruent and parallel

Volume = Surface Volume = Surface Area Area The sum of the areas The sum of the areas

of all the facesof all the faces

The ‘outside’ of the The ‘outside’ of the geometric figuregeometric figure

Use area formulasUse area formulas

Measured in square Measured in square inches, square feet…inches, square feet…

COUNT SQUARESCOUNT SQUARES

The measure of the The measure of the amount of space amount of space

contained in a solidcontained in a solid

The ‘inside’ of the The ‘inside’ of the geometric figuregeometric figure

Use volume formulasUse volume formulas

measured in cubic measured in cubic feet, cubic inches…feet, cubic inches…

COUNT CUBESCOUNT CUBES

Oblique Rectangular

Prism

Altitude = heightAltitude = height

Oblique CylinderAltitude = heightAltitude = height

Right Cylinder

Altitude

Term Definition ExampleVolume The measure of the amount

of space contained in a solidMeasured in cubic units

Prism/cylinder volume

conjecture

The volume of a prism or a cylinder is the area of the

base multiplied by the height V = ABASE∙ H

Volume

VolumeVolume

6

BASE is a TRAPEZOID! PRISMS have TWO bases that are PARALLEL and CONGRUENT

V = Abase∙H = ½ (b1 + b2) h ∙ H

V = ½ (10 + 34) (6) (20) = 2640 u3

VolumeVolume RectangularPrism

Triangular prism

2base r

H

base l w wl

H

Trap

ezoi

dal

pris

m

2b hbase

H

1 2

2h b b

base

H

V = AV = Abasebase∙ H∙ H

what about a cone?

DEMONSTRATION--- How many “conefuls” of water will it take to fill a cylinder of the same radius and height?

same height

congruent bases

same volume?

what about a pyramid?

DEMONSTRATION--- How many “pyramids-fuls” of water will it take to fill a prism with same base area and height?

same height

same base areasame volume?

Stud

y Sh

eet

VolumeVolume RectangularPrism

Triangular prism

2base r

Hbase l w

wl

H

Trapezoidal prism

12

base bh

H

1 212

base h b b

HCylinder Prism

Pyramid

2base r

Cone

V = AV = Abasebase∙ H∙ H

V = 1/3 Abase∙ H V = 1/3 Abase∙ H

practice

Complete problems on handout.Be prepared to share them with the class.

You have 25 minutes. This work will be collected for a classwork grade.

debrief

how is volume different that surface area?

how do you find the surface area of a cone? how did we find the volume formula for a cone? a pyramid?