This final review section is focused entirely on three-dimensional figures known as solids. In Chapter 14, you looked at each type separately. These practice questions will give you the opportunity to bring together different shapes and different ideas. Answer all the questions, and try to express your thinking as clearly as you can.
1. Find the number of faces of a polyhedron with 18 edges and 12 vertices.
2. Sketch a possible map for a triangular prism.
3. Find the surface area of hexagonal prism with a perimeter of 12 inches and a height of 3 inches.
4. Find the surface area of a cylinder with a radius of 8 cm and a height of 14 cm.
5. Find the volume of pentagonal prism if the bases are regular pentagons with a perimeter of 40 feet and apothems of 5.5 feet and the height of the prism is 12 feet.
6. Find the volume of a cylinder with a diameter of 28 inches and a height of 30 inches.
7. Find the slant height of a cone with a radius of 36 inches and a height of 77 inches.
8. Find the surface area of a pyramid, to the nearest tenth of a square centimeter, if the base is a regular octagon with a perimeter of 120 cm and an apothem of 18.1 cm and the height of the pyramid is 11 cm.
9. Find the surface area of a cone with a diameter of 18 inches and a height of 12 inches.
10. Find the volume of a square pyramid 4 feet on a side and 6 feet high.
11. Find the volume of a cone with a base circumference of 38π inches and a height of 21 inches.
12. Find the surface area of a rectangle prism that measures 2 feet by 8 feet by 15 feet.
13. Find the volume of a cone that has a surface area of 216π square centimeters if the slant height is 6 cm longer than the radius. Leave your answer in terms of π.
14. Find the height of a triangular pyramid whose base is an equilateral triangle with a perimeter of 12 inches, if the volume of the pyramid is 34 cubic inches.
15. Find the radius of a cylinder with a height of 5 meters and a surface area of 168π square meters.
16. A square pyramid with a perimeter of 40 cm has a surface area 360 square centimeters. Find its volume.
17. Which has the larger surface area: a cylinder with a diameter of 20 inches and height of 20 inches, or a cone with radius 15 inches and height of 36 inches?
18. The TransAmerica Pyramid, one of the tallest buildings in San Francisco, California, is not a true pyramid because it has “wings” that provide additional space for the narrower upper floors. The underlying pyramid shape has a base area of 65,225 square meters and the building has a height of 260 meters. Find the volume of the building, without its “wings,” to the nearest cubic meter.
19. The Coliseum in Rome, Italy, does not have a perfectly circular base, but is actually somewhat elliptical. The area of its base can be calculated nonetheless, using the formula for the area of an ellipse. If the area of the base is 79,515π square feet and the height is 157 feet, what is the volume of the structure?
20. Iron has a density of approximately 7.9 grams per cubic centimeter. A cylindrical disk with a diameter of 6 cm and a height of 2 cm is cast from iron. The same cylinder, cast in lead, has a mass 192 grams greater. To the nearest tenth, what is the density of lead?