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LESSON 12.1-12.3

Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning.

1. 2. 3.

Use Euler's Theorem to find the value of n.

4. Faces: n 5. Faces: 10 6. Faces: 14

Vertices: 4 Vertices: n Vertices: 24

Edges: 6 Edges: 24 Edges: n

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

7. 8. 9.

10. Visual Thinking An architect is designing a contemporary office building in the shape of a pyramid. The building will have eight sides. What is the shape of the base of the building?

Describe the cross section formed by the intersection of the plane and the solid.

11. 12. 13.

14. Multiple Choice Assume at least one face of a solid is congruent to at least one face of another solid. Which two solids can be adjoined by congruent faces to form a hexahedron?

A. A rectangular prism and a rectangular pyramid

B. A triangular pyramid and a triangular pyramid

C. A triangular prism and a triangular pyramid

D. A cube and a triangular prism

Find the surface area of the right prism. Round your answer to two decimal places.

15. 16. 17.

Find the surface area of the right cylinder using the given radius r and height h. Round your answer to two decimal places.

18. r = 5 cm; h = 15 cm 19. r= 1.1 ft; h = 3.2 ft 20. r = 12 in.; h = 18 in.

Solve for x given the surface area S of the right prism or right cylinder. Round your answer to two decimal places.

21. S= 320 m2 22. S = 200 ft2 23. S = 1000 cm2

24. Surface Area of a Prism A triangular prism with a right triangular base has one leg length that is 6 inches and the other leg length that is 8 inches. The height of the prism is 7 inches. What is the surface area of the prism?

25. Multiple Choice The radius and height of a right cylinder are each multiplied by 2. What is the change in the surface area of the cylinder?

a. The surface area is 2 times the original surface area.

b. The surface area is 4 times the original surface area.

c. The surface area is 6 times the original surface area.

d. The surface area is 8 times the original surface area.

26. Radius of a Cylinder Find the radius of a right cylinder with a surface area of 48( square feet. The height of the cylinder is 5 feet.

27. Candy Box As a birthday present for a friend, you buy a cylindrical box of candy. The diameter of the box is 6 inches and the height is 8 inches. What is the minimum amount of wrapping paper needed to wrap the gift? Round your answer to two decimal places.

Find the area of each lateral face of the regular pyramid. Round your answer to two decimal places.

1. 2.

Find the surface area of the regular pyramid. Round your answer to two decimal places.

3. 4.

Find the lateral area of the right cone. Round your answer to two decimal places.

5. 6.

Find the surface area of the right cone. Round your answer to two decimal places.

7. 8.

9. Multiple Choice The surface area of a regular pyramid with a square base is 1536 square meters. The base edge length is 24 meters and the slant height is 20 meters. What is the height of the pyramid?

A. 8 meters

B. 12 meters

C. 16 meters

D. 20 meters

Sketch the described solid.

10. A regular pyramid has a slant height of 12 inches. Its base is a square with a base edge length of 18 inches.

11. A right cone has a radius of 3 feet and a height of 9 feet.

Find the surface area of the solid. The pyramids are regular and the cones are right. Round your answer to two decimal places.

12. 13.

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