Geometry Test 5/13/11 - WPHS Green Wave Math - Geometry
Geometry Test 5/13/11
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the height of a rectangular prism with a 3 in. by 4 in. base and a 7 in. diagonal. Round to the nearest tenth.
|a. |24.0 in. |c. |4.9 in. |
|b. |74.0 in. |d. |8.6 in. |
____ 2. Find the distance between the points (11, 6, 12) and (12, 7, 17). Round to the nearest tenth.
|a. |39.2 units |c. |5.2 units |
|b. |3.0 units |d. |1.3 units |
____ 3. Find the lateral area and surface area of a regular triangular right prism with base edge 7 cm and height 11 cm. Round to the nearest tenth.
|a. |lateral area: [pic]; |c. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
|b. |lateral area: [pic]; |d. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
____ 4. Find the lateral area and surface area of the right cylinder. Give your answer in terms of [pic].
[pic]
|a. |lateral area: [pic]; |c. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
|b. |lateral area: [pic]; |d. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
____ 5. Find the surface area of the composite figure. Round to the nearest hundredth.
[pic]
|a. |66.17 [pic] |c. |41.82 [pic] |
|b. |48.69 [pic] |d. |61.26 [pic] |
____ 6. The length, width, and height of the right rectangular prism are tripled. Describe the effect on the surface area.
[pic]
|a. |The surface area is multiplied by 3. |
|b. |The surface area is multiplied by 9. |
|c. |The surface area is multiplied by 27. |
|d. |The surface area is multiplied by 81. |
____ 7. Find the lateral area and surface area of a regular square pyramid with base edge length 6 m and slant height 8 m.
|a. |lateral area: [pic]; |c. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
|b. |lateral area: [pic]; |d. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
____ 8. Find the lateral area and surface area of a regular triangular pyramid with base edge length 4 m and slant height 6 m.
|a. |lateral area: [pic]; |c. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
|b. |lateral area: [pic]; |d. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
____ 9. Find the lateral area and surface area of a right cone with radius 6 in. and height 8 in. Give your answers in terms of [pic].
|a. |lateral area: [pic]; |c. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
|b. |lateral area: [pic]; |d. |lateral area: [pic]; |
| |surface area: [pic] | |surface area: [pic] |
____ 10. The radius and slant height of the right cone are multiplied by [pic]. Describe the effect on the surface area.
[pic]
|a. |The surface area is multiplied by [pic]. |
|b. |The surface area is multiplied by [pic]. |
|c. |The surface area is multiplied by [pic]. |
|d. |The surface area is multiplied by [pic]. |
____ 11. Find the surface area of the composite figure. Round to the nearest square centimeter.
[pic]
|a. |550 cm2 |c. |725 cm2 |
|b. |656 cm2 |d. |814 cm2 |
____ 12. A frustum of a pyramid is a part of the pyramid with two parallel bases. The slant height of the frustum of the pyramid is half the slant height of the original square pyramid. Find the surface area of the original pyramid, the lateral area of the top of the pyramid, and the area of the top base of the frustum. Then, find the surface area of the frustum of the pyramid.
[pic]
|a. |Surface area of the original pyramid = 192 cm[pic]; Lateral area of the top of the pyramid = 48 cm[pic]; Area of the top|
| |base of the frustum = 9 cm[pic]; Surface area of the frustum of the pyramid = 153 cm[pic]. |
|b. |Surface area of the original pyramid = 228 cm[pic]; Lateral area of the top of the pyramid = 57 cm[pic]; Area of the top|
| |base of the frustum = 9 cm[pic]; Surface area of the frustum of the pyramid = 180 cm[pic]. |
|c. |Surface area of the original pyramid = 192 cm[pic]; Lateral area of the top of the pyramid = 57 cm[pic]; Area of the top|
| |base of the frustum = 9 cm[pic]; Surface area of the frustum of the pyramid = 144 cm[pic]. |
|d. |Surface area of the original pyramid = 228 cm[pic]; Lateral area of the top of the pyramid = 48 cm[pic]; Area of the top|
| |base of the frustum = 9 cm[pic]; Surface area of the frustum of the pyramid = 189 cm[pic]. |
____ 13. Find the volume of a right rectangular prism with length 12 in., width 10 in., and height 6 in. Round to the nearest tenth, if necessary.
|a. |240 in2 |c. |2,400 in3 |
|b. |720 in3 |d. |360 in3 |
____ 14. Find the volume of a right rectangular prism with length 13 in., width 8 in., and height 7 in. Round to the nearest tenth, if necessary.
|a. |728 in3 |c. |1,941.3 in3 |
|b. |364 in3 |d. |242.7 in2 |
____ 15. A fish tank is in the shape of a rectangular prism. The height of the tank is 18 in. The width of the tank is 17 in. The length of the tank is 38 in. Find the amount of water the tank can hold to the nearest gallon. (Hint: 1 gallon [pic] 0.134 ft3.)
|a. |7 gallons |c. |130 gallons |
|b. |50 gallons |d. |7,231 gallons |
____ 16. Find the volume of a cylinder with a base area of 25[pic] [pic] and height equal to the radius. Give your answer both in terms of [pic] and rounded to the nearest tenth.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 17. Find the volume of a cylinder with a base area of 36[pic] [pic] and height equal to the radius. Give your answer both in terms of [pic] and rounded to the nearest tenth.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 18. The radius and height of the cylinder are multiplied by 4. Describe the effect on the volume.
[pic]
|a. |The volume is multiplied by 4. |c. |The volume is multiplied by 16. |
|b. |The volume is multiplied by 8. |d. |The volume is multiplied by 64. |
____ 19. Find the volume of the composite figure. Round to the nearest tenth. (Hint: Volume of a cone is [pic].)
[pic]
|a. |88.0 cm3 |c. |75.4 cm3 |
|b. |12.6 cm3 |d. |28.0 cm3 |
____ 20. Find the volume of the three-dimensional figure in terms of x.
[pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 21. Find the volume of a rectangular pyramid with length 11 m, width 7 m, and height 8 m. Round to the nearest tenth, if necessary.
|a. |[pic] m3 |c. |[pic] m3 |
|b. |[pic] m3 |d. |[pic] m3 |
____ 22. Find the volume of a rectangular pyramid with length 12 m, width 10 m, and height 5 m. Round to the nearest tenth, if necessary.
|a. |[pic] m3 |c. |[pic] m3 |
|b. |[pic] m3 |d. |[pic] m3 |
____ 23. The base area of a model square pyramid is 1,000 sq ft. The height of the pyramid is 100 ft. Find the volume of the pyramid in cubic feet. Round to the nearest cubic foot.
|a. |100,000 ft3 |c. |100,000,000 ft3 |
|b. |33,333 ft3 |d. |1,054 ft3 |
____ 24. Find the volume of a cone with a base circumference of 19[pic] cm and a height 6 cm less than twice the radius. Give your answer both in terms of [pic] and rounded to the nearest tenth.
|a. |752.1π cm 3 ≈ 2,362.7 cm3 |c. |391.1π cm 3 ≈ 1,228.6 cm3 |
|b. |1,173.3π cm 3 ≈ 3,685.9 cm3 |d. |17.2π cm 3 ≈ 54.1 cm3 |
____ 25. Find the volume of the composite figure. Round to the nearest hundredth.
[pic]
|a. |28.26 ft3 |c. |113.04 ft3 |
|b. |84.78 ft3 |d. |197.82 ft3 |
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