Chapter 12 Review Period:

Transcription

1 Chapter 12 Review Name: Period: 1. Find the number of vertices, faces, and edges for the figure. 9. A polyhedron has 6 faces and 7 vertices. How many edges does it have? Explain your answer. 10. Find the surface area of the right prism. 2. Sketch (if possible) a nonconvex polyhedron.. Sketch (if possible) a polyhedron with faces. 4. Sketch (if possible) a polyhedron with 6 faces and 8 vertices. 48 m 40 m 42 m 5. Sketch (if possible) two different polyhedrons with 6 vertices. 11. Find the surface area of the right prism below. 6. Describe the cross section. 12. The right prism below has bases which are equilateral triangles of side length 4 cm. Its height is 5 cm. Find its surface area. 7. A polyhedron has 9 faces and 21 edges. How many vertices does it have? Explain your answer. 8. Use Euler s Theorem to calculate how many faces a polyhedron has if it has 6 edges and 4 vertices. 1. Calculate the surface area of a cylindrical water tank that is 7 m high and has a diameter of 10 m. Use π 14..

2 14. The figure shown below is a cylindrical solid with a circular cylindrical hole drilled out of the center. Find the surface area of the resulting solid. 18. The pyramid below has a square base and a slant height of 7 ft. Find its surface area. 19. A pyramid is in the form of a regular tetrahedron of edge length 2 in. Find its surface area. 15. Find the surface area of the right cylinder below. (Round the result to two decimal places.) 20. Find the surface area of the right cone below. (Round the result to two decimal places.) 16. Calculate the surface area of the lateral faces of a regular hexagonal pyramid that has a slant height of 5 cm and a base side length of 4 cm. 17. Find the surface area of the lateral faces on the regular pyramid below. 21. Find the surface area of the right cone below to two decimal places. [A] 168 ft 2 [B] 52 ft 2 [C] 84 ft 2 [D] 6 ft Find the surface area of a cone with height of cm and radius of 4 cm. Express the answer in terms of π. 2. Find the volume of the rectangular prism. 1 m m 2 m

3 24. Johannas is building a square sandbox with sides 9 feet long. He wants to put sand 0.95 feet deep in the box. How many cubic feet of sand should Johannas order? 0. Find the volume of the cylinder below. (Round the result to one decimal place.) 25. Ralph bought a generator that will run for 2 hours on a liter of gas. The gas tank on the generator is a rectangular prism with dimensions 12 centimeters by 10 centimeters by 20 centimeters as shown below. If Ralph fills the tank with gas, how long will the generator run? Show how you arrived at your answer. 1L = 1000 cm c h 1. Find the surface area and volume of the cylinder that can be folded from the net shown below. 10 cm 20 cm 12 cm 26. Find the exact volume of a cone that has a height of 9 inches and a radius of 5 inches. 27. Which has a greater volume: a cube of edge length x or a cylinder with height of x and diameter of x? Explain. 2. A cylindrical can is 20 cm in diameter and 16 cm in height. You want to reduce the diameter of the can to 16 cm. What must the height be if the new can still has the same volume? Explain your answer. 28. Find the volume of a cylinder with height 6. m and diameter 4 m. Use π Find the volume of the right prism below.

4 . The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume. 7. Find the volume of a right cone with slant height of 85 cm and radius of 77 cm. Express in terms of π. 8 ft 8. The base of the pyramid below is a nonregular heptagon with an area of 0.0 square yards. The height of the pyramid is 6.6 yards. Find the volume of the pyramid. 6 ft 2 ft 4. The volume of the pyramid below is. 9. A solid consists of a cylinder attached at one base to an off-center cone as shown below. Write a formula for the volume enclosed. [A] 78 ft [B] 195π ft [C] 126 ft [D] 126π ft 5. The base of the pyramid is a parallelogram with dimensions as shown below. Find the volume of the pyramid to the nearest tenth of a cubic inch. 40. A machinist drilled a conical hole into a cube of metal as shown. If the cube has sides of length 5 cm, what is the volume of the metal after the hole is drilled? Use π 14. and round to the nearest tenth. 6. Calculate the volume of a cone with height 6 feet and radius 5 feet. 41. Find the diameter of a sphere that has a surface area of 196π in 2.

5 42. Find the surface area of a sphere that has a diameter of 8 centimeters. Express your answer in terms of π. 49. Find the volume of a sphere with a radius of 17. inches in cubic feet to the nearest tenth of a cubic foot. 4. Find the surface area to the nearest tenth of a square inch of a sphere that has a radius of 17. inches. 44. A company has a spherical storage tank which is in need of painting. The radius of the tank is 5.4 ft. The type of paint used will cover approximately 160 ft 2 per gallon. How many gallons of paint will be needed? (Round decimal to the higher whole number of gallons.) 50. Find the volume, to the nearest cubic foot, of a sphere whose surface area is 100 ft A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside the cylinder to the nearest tenth of a cubic inch. 45. What is the area of a great circle of a sphere that has a surface area of 44.8 square yards? The areas of corresponding faces of two similar triangular prisms are 144 cm and 25 cm. What is the ratio of the corresponding side lengths? of the perimeters of the corresponding faces? of the volumes? Use the figure above.the surface area of the sphere is about. 5. The surface area of a sphere is 200 cm 2. If the radius were three times as large, what would the surface area be? [A] 92.5 ft 2 [B] 44.9 ft 2 [C] 69.4 ft 2 [D] ft A satellite is made of a cylinder and two hemispheres. The hemispheres have the same radius as the cylinder and each fit snugly on either end of the cylinder. If the diameter of the cylinder is 4m and its length is 18 m, find the volume of the satellite. Leave your answer in terms of π. 48. Find the volume of a sphere 10 ft in diameter. Use π 14. and round your answer to the nearest tenth.

6 54. The shipping crates shown are similar. A. Find the similarity ratio of the crate on the left to the crate on the right. B. Find the ratio of their surface areas. C. Find the ratio of their volumes

7 Reference: [ ] [1] 7 vertices, 7 faces, 12 edges Reference: [ ] Sketches vary. [2] Reference: [ ] [] Not possible. Reference: [ ] Sketches vary. [4] Reference: [ ] Sketches vary. [5] Reference: [ a] [6] Pentagon Reference: [ ] [7] 14, because F + V = E + 2 and = Reference: [ ] [8] 4 Reference: [ ] E = 11; 11, because F + V = E + 2 and = [9] Reference: [ ] [10] 7968 m 2 Reference: [ ] [11] 54 in. 2 Reference: [ ] [12] d i cm 7. 9 cm Reference: [ ] [1] 768. m Reference: [ ] [14] 24 π in in. 2 Reference: [ ] [15] 80π cm cm 2 Reference: [ ] [16] cm Reference: [ ] [17] [D] Reference: [ ] [18] 95 ft 2 Reference: [ ] [19] 4 in. 69. in. Reference: [ ] [20] π cm cm Reference: [ ] d [21] π cm cm Reference: [12..2.] [22] 6 π cm 2 Reference: [ ] [2] 6 m i

8 Reference: [ ] [24] ft Reference: [ ] The gas tank has a volume of 2400 cm which is equal to 2.4 liters. Multiplying by 2 hours [25] gives 4.8 hours or 4 hours 48 minutes. Reference: [ a] [26] 15 π in Reference: [ ] The cube; the cube has volume of x while the cylinder has volume of π x [27] 4 Reference: [ ] [28] 79.1 m Reference: [ ] [29] 825 in. Reference: [ ] [0] π ft ft Reference: [ ] 2 [1] Area: 6π ft, Volume: 2π ft 079. x. Reference: [ ] 25 cm; Volume of each can = 1600π ; so [2] 1600π = 64π h and h = 25. Reference: [ ] [] 2 ft Reference: [ ] [4] [C] Reference: [ ] [5] in. Reference: [ ] [6] 50π ft Reference: [ ] [7] 71,148 π cm Reference: [ ] [8] 66 yd Reference: [ ] [9] V = 4 r 2 π h Reference: [ ] [40] 92. cm Reference: [ ] [41] 14 in. Reference: [ ] [42] 64 π cm 2 Reference: [ ] [4] π in in. Reference: [ ] [44] 99 gallons Reference: [ ] [45] 11.2 yd 2 Reference: [ ] [46] [D]

9 Reference: [ ] [47] π m Reference: [ ] [48] 52. ft Reference: [ ] b [49] π 5184 ft ft Reference: [ ] [50] π ft 94 ft g Reference: [ ] 11 π in in. [51] Reference: [ ] [52] 12:5; 12:5; 1728:125 Reference: [ ] [5] 1800 cm 2 Reference: [ ] 7 49 A., B., C. [54]