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GEOMETRY CHAPTER 12

SURFACE AREA AND VOLUME OF SOLIDS

Unit 1 Explore Solids

1. Explain why a cube is also called a regular hexahedron.

2. Sketch the polyhedron.

a. rectangular prism b. Square pyramid

3. Use Euler’s Theorem to find the value of n.

a. Faces: n b. Faces: 5

Vertices: 12 Vertices: n

Edges: 18 Edges: 8

4. Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem.

a. b.

Unit 2 Surface Area of Prisms and Cylinders

1. Find the surface area of the solid formed by the net.

a. b.

2. Find the surface area of the right prism.

a. b.

3. Solve for x given the surface area of the right prism or cylinder.

a. S = 320m2 b. S = 1000 cm2

Unit 3 Surface Area of Pyramids and Cones

1. Draw a regular square pyramid. Label its height, slant height, and base.

2. Find the area of each lateral face of the regular pyramid.

a. b.

3. Find the surface area of the regular pyramid.

a. b.

4. Find the surface area of the right cone.

a. b.

Unit 4 Volume of Prisms and Cylinders

1. Two solids have the same volume. Do they also have the same surface area? Explain your reasoning.

2. Find the volume of the solid.

a. b.

3. Find the volume of the right prism or cylinder.

a. b.

4. Find the volume of the oblique prism or cylinder.

a. b.

Unit 5 Volume of Pyramids and Cones

1. Explain the difference between a triangular prism and a triangular pyramid. Draw an example of each.

2. Find the volume of the solid.

a. b.

3. Find the value of x.

a. V = 64 in.3 b. V = 147( cm3

4. Find the volume of the right cone.

a. b.

Unit 6 Surface Area and Volume of Spheres

1. Find the surface area of the sphere.

a. b.

2. Find the volume of the two spheres above.

a. b.

3. Find the radius of the sphere with the given volume.

a. V = 1436.76 m3 b. V = 91.95 cm3

4. Tennis balls are stored in a cylindrical container with height 21 centimeters and diameter 7 centimeters. Three tennis balls fit in one container.

a. Find the volume of the container.

b. Find the volume of a tennis ball.

c. Find the percentage of the container taken up by the tennis balls.

Unit 7 Explore Similar Solids

1. What does it mean for two solids to be similar?

2. Solid A (shown) is similar to solid B (not shown) with the given scale factor A:B. Find the surface area and volume of solid B.

a. Scale factor of 1:2 b. Scale factor of 2:3

3. Solid A is similar to solid B. Find the scale factor of solid A to solid B.

a. b.

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