Volume review. 1. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches.

Transcription

1 Name: ate: 1. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. 3. Which diagram represents the figure with the greatest volume? A.... What is the volume of the cone to the nearest cubic inch? A A storage container in the shape of a right circular cylinder is shown in the accompanying diagram. 2. If the surface area of a sphere is represented by 144π, what is the volume in terms of π? A. 36π. 48π. 216π. 288π What is the volume of this container, to the nearest hundredth? A in in in in 3 page 1

2 5. A cylinder has a diameter of 10 inches and a height of 2.3 inches. What is the volume of this cylinder, to the nearest tenth of a cubic inch? A How many cubes with 5-inch sides will completely fill a cube that is 10 inches on a side? A A cube whose edge has a length of 4 has the same volume as a rectangular box whose length is 8 and whose width is 4. The height of the rectangular box is A The volume of a cylindrical can is 32π cubic inches. If the height of the can is 2 inches, what is its radius, in inches? A A block of wood is 5 inches long, 2 inches wide, and 3 inches high. What is the volume of this block of wood? A. 10 in in in in The volume of a cube is 64 cubic inches. Its total surface area, in square inches, is A What is the volume of a cube whose edge has a length of 4? A If the volume of a cube is 8 cubic centimeters, what is its surface area, in square centimeters? A page 2

3 13. To calculate the volume of a small wooden cube, Ezra measured an edge of the cube as 2 cm. The actual length of the edge of Ezra s cube is 2.1 cm. What is the relative error in his volume calculation to the nearest hundredth? A A box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box? A in. 16 in. 8 in. 4 in 14. Which expression represents the volume, in cubic centimeters, of the cylinder represented in the diagram below? 17. A side of a cube measures 4 centimeters and a side of a smaller cube measures 2 centimeters. The volume of the larger cube is how many times the volume of the smaller cube? A A. 162π. 324π. 972π. 3, 888π 18. The volume, in cubic centimeters, of a sphere whose diameter is 6 centimeters is A. 12π. 36π. 48π. 288π 15. What is the volume, in cubic centimeters, of a cylinder that has a height of 15 cm and a diameter of 12 cm? A. 180π. 540π. 675π. 2,160π 19. A right circular cylinder has a base whose area is 12π. If the height of the cylinder is 6, the volume of the cylinder is A. 18π. 24π. 36π. 72π page 3

4 20. If the edge of a cube is 6 centimeters and the edge of a second cube is 5 centimeters, the difference in the volumes of these cubes is A. 1 cm cm What is the volume of a rectangular solid with a length of 12, a width of 3, and a height of 4? A cm cm The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch? 24. A sphere is inscribed inside a cube with edges of 6 cm. In cubic centimeters, what is the volume of the sphere, in terms of π? A. 12π. 36π. 48π. 288π A , A packing carton in the shape of a triangular prism is shown in the diagram below. 25. The volume of a sphere is approximately cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter? A What is the volume, in cubic inches, of this carton? A Two prisms have equal heights and equal volumes. The base of one is a pentagon and the base of the other is a square. If the area of the pentagonal base is 36 square inches, how many inches are in the length of each side of the square base? A page 4

5 27. Two prisms with equal altitudes have equal volumes. The base of one prism is a square with a side length of 5 inches. The base of the second prism is a rectangle with a side length of 10 inches. etermine and state, in inches, the measure of the width of the rectangle. 32. A regular pyramid with a square base is shown in the diagram below. 28. A right prism has a square base with an area of 12 square meters. The volume of the prism is 84 cubic meters. etermine and state the height of the prism, in meters. A side, s, of the base of the pyramid is 12 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic meters? 29. A right circular cylinder with a height of 5 cm has a base with a diameter of 6 cm. Find the lateral area of the cylinder to the nearest hundredth of a square centimeter. Find the volume of the cylinder to the nearest hundredth of a cubic centimeter. 33. The diagram below represents Joe s two fish tanks. 30. A cylinder has a height of 7 cm and a base with a diameter of 10 cm. etermine the volume, in cubic centimeters, of the cylinder in terms of π. Joe s larger tank is completely filled with water. He takes water from it to completely fill the small tank. etermine how many cubic inches of water will remain in the larger tank. 31. A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, in terms of π. page 5

6 34. Tracey has two empty cube-shaped containers with sides of 5 inches and 7 inches, as shown in the accompanying diagram. She fills the smaller container completely with water and then pours all the water from the smaller container into the larger container. How deep, to the nearest tenth of an inch, will the water be in the larger container? 36. eborah built a box by cutting 3-inch squares from the corners of a rectangular sheet of cardboard, as shown in the accompanying diagram, and then folding the sides up. The volume of the box is 150 cubic inches, and the longer side of the box is 5 inches more than the shorter side. Find the number of inches in the shorter side of the original sheet of cardboard. 35. As shown in the accompanying diagram, the length, width, and height of Richard s fish tank are 24 inches, 16 inches, and 18 inches, respectively. Richard is filling his fish tank with water from a hose at the rate of 500 cubic inches per minute. How long will it take, to the nearest minute, to fill the tank to a depth of 15 inches? 37. Tina s preschool has a set of cardboard building blocks, each of which measures 9 inches by 9 inches by 4 inches. How many of these blocks will Tina need to build a wall 4 inches thick, 3 feet high, and 12 feet long? 38. A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width of the tank are 14 inches and 12 inches, respectively. Find the height, in inches, of the tank. page 6

7 39. In the accompanying diagram, a rectangular container with the dimensions 10 inches by 15 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. What is the maximum number of full cups of water that can be placed into the container without the water overflowing the container? 43. Find the number of cubic units in the volume of a cube whose edge measures 4 units. 44. The volume of a rectangular solid is 80 cubic centimeters, the length is 2 centimeters, and the width is 4 centimeters. Find the number of centimeters in the height of the rectangular solid. 40. Tamika has a hard rubber ball whose circumference measures 13 inches. She wants to box it for a gift but can only find cube-shaped boxes of sides 3 inches, 4 inches, 5 inches, or 6 inches. What is the smallest box that the ball will fit into with the top on? 45. The volume of a rectangular solid is 24 cubic centimeters. If the width is 2 centimeters and the length is 3 centimeters, what is the height, in centimeters, of the solid? 41. The volume of a rectangular pool is 1,080 cubic meters. Its length, width, and the depth are in the ratio 10 : 4 : 1. Find the number of meters in each of the three dimensions of the pool. 46. The length of a rectangular solid is 3.0 meters, the width is 0.6 meter, and the height is 0.4 meter. Find, to the nearest tenth, the number of cubic meters in the volume of the solid. 42. The dimensions of a brick, in inches, are 2 by 4 by 8. How many such bricks are needed to have a total volume of exactly 1 cubic foot? 47. If the volume of a cube is 64 cubic centimeters, how many centimeters are in the length of an edge of the cube? page 7

8 48. The volume of a rectangular solid is 180 cubic centimeters. The length is 10 centimeters and the width is 4 centimeters. Using the formula V = lwh, find the number of centimeters in the height. 49. The length of an edge of a cube is 2 inches. How many cubic inches are there in the volume of the cube? 50. What is the volume, in cubic centimeters, of a cube whose edge measures 2 centimeters? page 8

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