Geometry Name: _______________________________________ Review 13 – 1 to 13 – 3 Period: _________ Date: ____________________ Find the volume of each prism or cylinder. Round to the nearest tenth if necessary. 1. 2. 3. 4. AQUARIUM. For Exercises 5 – 7, use the following information. Round answers to the nearest tenth. Mr. Gutierrez purchased a cylindrical aquarium for his office. The aquarium has a height of 25 ½ inches and a radius of 21 inches. 5. What is the volume of the aquarium in cubic feet? 6. If there are 7.48 gallons in a cubic foot, how many gallons of water does the aquarium hold? 7. If a cubic foot of water weighs about 62.4 pounds, what is the weight of the water in the aquarium to the nearest five pounds? Find the volume of each pyramid or cone. Round to the nearest tenth if necessary. 8. 9. 10. 11. 12. CONSTRUCTION. Mr. Ganty built a conical storage shed. The base of the shed is 4 meters in diameter, and the height of the shed is 3.8 meters. What is the volume of the shed? 13. HISTORY. The start of the pyramid age began with King Zoser’s pyramid, erected in the 27th century B.C. In its original state, it stood 62 meters high with a rectangular base that measured 140 meters by 118 meters. Find the volume of the original pyramid. Find the volume of each sphere or hemisphere. Round to the nearest tenth. 14. The radius of the sphere is 12.4 centimeters. 15. The circumference of the sphere is 38 meters. 16. The diameter of the hemisphere is 21 inches. 17. 18. 19. PACKAGING. Amber plans to ship a mini-­‐basketball she bought for her nephew. The circumference of the ball is 24 inches and the package she wants to ship it in is a rectangular box that measures 8 inches x 8 inches x 9 inches. Will the basketball fit in the box? Explain. 20. A cube has a volume of 4096 in3. Find its lateral area. 21. Given a box with dimensions of 8 cm, 5 cm, and 12 cm find the surface area and volume of the box. 22. Consider the square pyramid below. a. Find the area of the base. b. Find the surface area. c. Find its volume. Round to the nearest tenth. 23. Consider the cone below. a. Find the surface area. b. Find the volume. 24. A pyramid has a square base. Its volume is 192 inches. If the length of a base edge is 8 inches, what is the height? 25. Name all solids from the following list for which each volume formula can be used: prism, pyramid, cone, cylinder, sphere, hemisphere. a. V = Bh b. V = (4/3)πr3 c. V = (1/3)Bh d. V = πr2h e. V = (1/3)πr2h f. V = (2/3)πr3 26. Let r represent the radius and d represent the diameter of a sphere. Determine whether each formula below can be used to find the volume of a sphere, a hemisphere, or neither. 2! r 3
a. V = 3 b. V = (1/6)πd3 c. V = (1/3)πr3 d. V = ¾ πr3 !d3
e. V = 12 f. V = (4/3)πr2h 27. Compare the volumes of these three solids. Then complete the sentence below. Of the three solids shown above, the __________________ has the largest volume and the _______________ has the smallest volume.