Surface Area and Volume Notes.notebook

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Mar 7­1:22 PM

1.

Warm-Up

2.

D.4.a - Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems D.4.b - Describe and draw cross sections of prisms, cylinders, pyramids, and cones E.1.f - Apply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real-world problems E.1.h - Identify and give properties of congruent or similar solids F.2.a - Find the lateral area, surface area, and volume of prisms, cylinders, cones, and pyramids in mathematical and real-world settings F.2.b - Use cross sections of prisms, cylinders, pyramids, and cones to solve volume problems F.2.c - Find the surface area and volume of a sphere in mathematical and real-world settings

3. What is the equation of the circle with a center of (-2,4) and a radius of 3.5?

Review Problem

Mar 7­1:28 PM

3D Figures

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Mar 8­10:43 AM

Solid: a three dimensional figure

Polyhedron: 3-D figure whose surfaces are polygons.1. face: the polygons that make up the polyhedron2. edge: the line segments form by the intersection of the two

faces.3. vertex: a point where 3 or more edges meet

Net- two dimensional plan/layout you fold to form a 3-D figure

Cross-section - the intersection of a solid and a plane. (think of it as a very thin slice of the solid.)

9.1 - Exploring Solids

Axis of rotation - rotating a two-dimensional shape about a line.

Mar 8­11:16 AM

Warm-Up

HW: pg. 692 #6-14 (even), 18-20, 31, 32

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Three-Dimensional solids can be created by stacking thin slices of 2D figures, or by rotating 2D shapes.

3D Solids:

Prism- A polyhedron with two congruent and parallel faces which are called the bases; the other faces (which are parallelograms) are called the lateral faces.

Bases- parallel faces in a prism

Cylinder - a three dimensional figure with two congruent circular bases laying in parallel planes.

Pyramid - a polyhedron in which one face, the base, is a polygon and the other faces, the lateral faces, are triangles with a common vertex.

Cone- a three dimensional figure that has a circular base, a vertex not in the plane of the base, and a curved lateral surface.

Sphere - the set of all points in space that are a given distance r(radius) from a given point c (center).

9.1 Continued

Mar 8­11:27 AM

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Mar 8­11:27 AM

Warm-Up1. Define a polyhedron.

2. Give three examples of 3D figures.

D.4.a - Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems D.4.b - Describe and draw cross sections of prisms, cylinders, pyramids, and cones E.1.f - Apply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real-world problems E.1.h - Identify and give properties of congruent or similar solids F.2.a - Find the lateral area, surface area, and volume of prisms, cylinders, cones, and pyramids in mathematical and real-world settings F.2.b - Use cross sections of prisms, cylinders, pyramids, and cones to solve volume problems F.2.c - Find the surface area and volume of a sphere in mathematical and real-world settings

Given a solid, students will be able to identify and classify the solid. Students will also be able to describe and draw a cross section of the solid. Given a solid, students will be able to use Euler’s theorem to determine the number of faces, edges and vertices of a solid. Given a solid, students will apply formulas to find the surface area of the figure. Given a solid, students will be able to apply formulas to find the volume of a solid.

Review3. What is the equation of the circle with a center at (-2,3) and a point on the circle (3,0)?

Mar 8­1:33 PM

9.2 Surface Area of Prisms and CylindersSurface Area- the sum of the areas of the faces of a figure

Lateral Faces ­ the faces of a prism that are not considered a baseAltitude ­ the perpendicular segment that joins the planes of the bases. The length of this segment is the height.Lateral Area ­ the sum of the areas of the lateral faces.Right Prism ­ a prism whose edge is an altitudeOblique prism ­ a prism whose altitude is not an edge.

One way to find the surface area is to use a net:

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Mar 10­6:53 AM

Formulas- Surface Area

Prism SA = 2B + Ph B = area of base P = perimeter of base

h = height of prism

Cylinder SA = 2πr2 + 2πrh r = radius h = height of cylinder

Mar 10­7:37 AM

Find the Surface Area of the prisms below

Surface Area and Volume Notes.notebook

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Mar 10­8:35 AM

YOU TRY!!

Mar 10­7:42 AM

Find the Surface Areas of the cylinders below

A cylinder has a height of 9 cm and a radius of 10 cm. What is the surface area of the cylinder in terms of π?

YOU TRY

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Mar 10­8:36 AM

Check for understandingpg. 704 #7-9, 11-13, 17-20, 33-35

Mar 10­10:04 AM

Warm-Up1.

2. Find the equation of the circle with points on the diameter of the circle (-2,8) and (4, 4).

Review

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Apr 25­1:13 PM

What is the surface area of the prism? Round your answer to the nearest whole number.

Mar 10­10:08 AM

RECALL:Pyramid - a polyhedron in which one face, the base, is a polygon and the other faces, the lateral faces, are triangles with a common vertex.

Cone- a three dimensional figure that has a circular base, a vertex not in the plane of the base, and a curved lateral surface.

Sphere - the set of all points in space that are a given distance r(radius) from a given point c (center).

9.3 - Surface Area of Pyramids, Cones, and Spheres

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Mar 10­10:14 AM

Formulas- Surface Area Pyramid SA = B + 1/2 Pl B = area of base P = perimeter of base

l = slant height of pyramid

EX1: Find the Surface area of the figures below.

The Pyramid of Cestius is located in Rome, Italy. Using the dimensions in the figure below, what is the surface area of the Pyramid of Cestius? Round to the nearest square meter?

YOU TRY!

Mar 10­11:34 AM

Cone SA = πr2 + πrl r = radius l = slant height of cone

EX 2- What is the surface area of the cone. Leave answers in terms of pi.

In a chemistry lab experiment, you use the conical filter funnel shown below. What is the surface area of the funnel?

YOU TRY!

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Mar 10­11:30 AM

Sphere SA = 4πr2

r = radius

EX 3: Find the surface area of the sphere

**Circumference = 2πr**Ex. Given that a softball has a circumference of 12 inches, find the surface area.

Mar 10­11:36 AM

Closing Activity: Whiteboards

Find the surface area of each figure. Raise your hand to get your answer checked before you leave!

HW: pg. 712-713 #8-11, 19-21, 26pg. 737 #6-16(even)

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Mar 10­2:41 PM

Warm-Up1.

2.

Review3. Write the equation of the circle with points on the diameter (-3,-5) and (4, 7).

May 13­1:22 PM

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May 13­1:34 PM

May 13­1:34 PM

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May 10­10:43 AM

May 10­2:42 PM

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May 10­9:11 AM

Apr 22­2:43 PM

Warm-Up1.

2. What is volume? How do we find volume?

Review Problem

3.

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May 14, 2019

Mar 10­2:43 PM

Warm-Up

D.4.a ­ Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problemsD.4.b ­ Describe and draw cross sections of prisms, cylinders, pyramids, and conesE.1.f ­ Apply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real­world problemsE.1.h ­ Identify and give properties of congruent or similar solidsF.2.a ­ Find the lateral area, surface area, and volume of prisms, cylinders, cones, and pyramids in mathematical and real­world settingsF.2.b ­ Use cross sections of prisms, cylinders, pyramids, and cones to solve volume problemsF.2.c ­ Find the surface area and volume of a sphere in mathematical and real­world settingsGiven a solid, students will be able to identify and classify the solid. Students will also be able to describe and draw a cross section of the solid. Given a solid, students will be able to use Eulers theorem to determine the number of faces, edges and vertices of a solid. Given a solid, students will apply formulas to find the surface area of the figure. Given a solid, students will be able to apply formulas to find the volume of a solid.

Mar 10­2:44 PM

9.4 Volumes of Prisms and Cylinders

B = area of baseh = height

Volume- the space that a three-dimensional figure occupies

V=Bh

What would that be for a cylinder???

Practice:

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Cavalieri's Principle:If two space figures have the same height and the same cross-sectional area at every level, then they have the same volume.

What is the approximate volume of the bullnose aquarium to the nearest cubic inch?

Composite space figures- a 3D figure that is the combination of two or more simpler figures.

Mar 10­3:47 PM

Closing ActivityWhat is the relationship between the a cylinder and the a cone? What about a square prism and a square pyramid?

What are the units for surface area? Volume?

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Mar 10­2:46 PM

Volume of a cone videohttp://www.teachertube.com/viewVideo.php?video_id=102103

9.5 Volumes of Pyramids, Cones and Spheres

V= (1/3)Bhr = 8cmheight = 12 cm

Mar 16­7:19 PM

Volume of Spheres

V= (4/3)πr3

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May 14, 2019

Mar 10­4:30 PM

Closing Activity

9.4: pg. 721 #6-18 (even)9.5: pg. 729 #6-18 (even), 22 pg. 737 #18-24 (even), 50

What is the volume of each figure below?

Mar 10­8:43 AM

Clarifications from Volume and Surface Area?

Any Questions?

Recall our lesson on Perimeters and Areas of similar figures.

What did we learn?

Ratio of Sides Ratio of Perimeters Ratio of Areas

If the two squares shown are similar, what is the ratio of their perimeter and area? 8 cm

3 cm

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Mar 10­4:49 PM

Let's see what it does to Surface Area and Volume

Similar Solids have the same shape, and all their corresponding dimensions are proportional.

Any two cubes are similar, as are any two spheres.

9.6 - Similar Solids

Dimensions Ratio of sides Ratio of Area Ratio of SA Ratio of Volume

3x4x5

6x8x10

12x16x20

Area and Volume RatiosIf the ratio of the sides is a:b, then the ratio of:The surface areas will be a2:b2

The volumes will be a3:b3

Mar 10­4:57 PM

Example 1:

Are the two rectangular prisms similar? If so, what is the similarity ratio of the first figure to the second figure?

Example 2: The square prisms at the right are similar. What is the similarity ratio of the smaller prism to the larger prism?

Example 3: What is the similarity ratio of two similar prisms with surface areas 144 in2 and 324 in2?

Example 4:The surface areas of two similar paint cans are 1764 cm2 and 400 cm2. The volume of the smaller can is 1157 cm3. What is the volume of the larger can?

Example 5: The volumes of two similar solids are 128 m3 and 250 m3. The surface area of the larger solid is 250 m2. What is the surface area of the smaller solid?

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Apr 8­10:20 AM

Using Scale Factor to find Capacity

A bottle that is 10 in high holds 34 oz of milk.The sandwich shop shown at the right is shaped like a milk bottle. To the nearest thousand ounces, how much milk could the building hold?

Using Scale Factor to find Capacity

A marble paper weight shaped like a pyramid weighs 0.15 lb. How much does a similarly shaped marble paper weight weigh if each dimension is 3 times as large?

Using Scale Factor to find Capacity

There are 650 toothpicks in a regular­sized box. If a jumbo box is made by tripling all the dimensions of the regular­sized box, how many toothpicks will the jumbo box hold?

ratio of sides ratio of volumes