12-7 Volume of Pyramids, Cones, and Spheres

Transcription

1 in mm mm ft cm ft yd 3 5. Amber purchased a necklace that contained an 8 millimeter diameter round pearl. Find the volume of the pearl to the nearest tenth mm 3 6 ft 3 esolutions Manual - Powered by Cognero Page 1

2 in A cone-shaped icicle is 2.5 feet long and has a diameter of 1.5 feet. a. Find the amount of ice in the icicle to the nearest tenth of a cubic foot. b. The icicle melts at a rate of 0.1 cubic foot every 5 minutes. How long will it take for the icicle to melt? a. 1.5 ft 3 b. about 75 min or 1 h 15 min Find the height of each figure. Round to the 18. square pyramid: volume m 3, length 12.6 m 16.5 m 19. cone: volume ft 3, diameter 8 ft 4.3 in pentagonal pyramid: base area 52 in 2, height 12 in. 208 in rectangular pyramid: length 3.5 feet, width 2 feet, height 4.5 feet 10.5 ft ft cm cone: diameter 6.7 mm, height 2.1 mm 24.7 mm sphere: radius 7.2 km km sphere: diameter 1.8 mm 3.1 mm in 3 esolutions Manual - Powered by Cognero Page 2

3 ,907.1 ft The solid silver bead shown is made of a cylinder and two cones. If pure silver s mass is 10.5 grams per cubic centimeter, find the approximate mass in grams of the bead. Round to the nearest gram. 26. Identify Structure Name the dimensions of two different cones whose volume is between 45 cubic inches and 55 cubic inches. Sample answer: r = 5 in., h = 2 in,; r = 3 in., h = 5 in. 27. Persevere with Problems A cone contains 93 cubic units of water. All the water is poured equally into three congruent cylindrical containers to a level of 4.5 units. What is the diameter of each container? Round to the nearest tenth. 3.0 units 28. Which One Doesn't Belong? Find the expression that does not represent the height of a threedimensional figure. Explain your reasoning g 24. The volume of a mini-basketball is about 230 cubic inches. What is its radius? Round to the nearest inch. 4 in. 25. Persevere with Problems Three golf balls are packaged in a box as shown. Round each answer to the nearest tenth. a. If each ball is 4.3 centimeters in diameter, find the volume of the empty space in the box. b. What percent of the box is full? ; Sample answer: When finding the height of a cone, the expression should be. 29. Identify Structure True or false? The volumes of a rectangular-based pyramid and a cone with the same height and equal areas of the base are equal. Explain your reasoning. a cm 3 b. 47.1% True; Sample answer: Both volumes are. esolutions Manual - Powered by Cognero Page 3

4 30. Persevere with Problems Which has a greater effect on the volume of a cone: changing the radius or changing the height? Explain. Sample answer: Changing the radius has a greater effect on the volume. If you double the radius, the volume is multiplied by 4. If you double the height, the volume is doubled. 31. Building on the Essential Question Write a realworld example where you would want to change a cylinder to a cone. Describe how the dimensions of the cone would be affected if the volumes remain the same. changing the shape of packaging; If the volumes remained the same and the packages have congruent bases, the cone s height would be 3 times the height of the cylinder. 32. What is the volume of a square pyramid with a height of 12 centimeters and base edges of 4 centimeters? A 48 cm 3 B 64 cm 3 C 96 cm 3 D 192 cm 3 B 33. Find the volume of the cone. Use 3.14 for π. Round to the nearest hundredth. 34. Short Response The volume of a cone is 3768 cubic millimeters. The radius of the base is 5 millimeters. Find the height of the cone mm 35. A sphere has a radius of 5 meters. Which of the following is closest to the volume of the sphere in cubic meters? A 65.4 m 3 B m 3 C m 3 D m 3 D in 3 F ft 3 G ft 3 H ft 3 J ft cm 3 H esolutions Manual - Powered by Cognero Page 4

5 38. Find the area of each figure. Round to the ft An elevator picks up a passenger 268 feet above ground and the door opens at the parking garage 48 feet below ground. How far did the elevator travel? 316 ft 40. Copy and complete the table. Use the results to write four solutions of y = x + 5. Write the solutions as ordered pairs ft m cm Find P(not prime) when you roll a 6-sided number cube. Then describe the likelihood of the event. Write impossible, unlikely, equally likely, likely, or certain. 0.5; equally likely ( 3, 2), ( 1, 4), (0, 5), (1, 6) 41. Manuel has $15 to buy snack mix that costs $5.75 per pound. Write and solve an equation to find the amount of snack mix he can buy if he spends all $15. Round to the nearest tenth. 5.75p = 15; 2.6 lb esolutions Manual - Powered by Cognero Page 5