Name: ate: 1. 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? 3. 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. 2. 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. 4. box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box?. 21.3 in. 16 in. 8 in. 4 in page 1
5. Which diagram represents the figure with the greatest volume? 7. storage container in the shape of a right circular cylinder is shown in the accompanying diagram..... What is the volume of this container, to the nearest hundredth?. 56.55 in 3. 125.66 in 3. 251.33 in 3. 502.65 in 3 6. s 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? 8. 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? page 2
9. The diagram below represents Joe s two fish tanks. 11. regular pyramid with a square base is shown in the diagram below. 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. 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? 10. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. 12. If the surface area of a sphere is represented by 144π, what is the volume in terms of π? What is the volume of the cone to the nearest cubic inch?. 36π. 48π. 216π. 288π. 201. 481. 603. 804 page 3
13. packing carton in the shape of a triangular prism is shown in the diagram below. 16. The volume of a sphere is approximately 44.6022 cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter?. 2.2. 3.3. 4.4. 4.7 What is the volume, in cubic inches, of this carton?. 20. 60. 120. 240 17. 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. 14. The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch? 18. The circumference of a circle is represented by 2πr. If the radius of the circle is doubled, then the circumference is. 706.9. 1767.1. 2827.4. 14,137.2. multiplied by 4. increased by 2. squared. doubled 15. 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?. 12π. 36π. 48π. 288π 19. If the length of each side of a triangle is doubled, then its perimeter. remains the same. is multiplied by 2. is multiplied by 4. is increased by 4 page 4
20. If the edge of a cube is doubled, the volume is multiplied by. 6. 2. 3. 8 25. The volume of a pyramid is equal to 1 3 the product of the altitude and the area of the base. If the area of the base remains the same and the altitude is doubled, the volume will. remain the same. double. triple. be multiplied by 4 21. If the length of any rectangle is increased by 2 and the width is unchanged, the perimeter is. increased by 2. multiplied by 2. increased by 4. multiplied by 4 26. If each side of a square is doubled, the area of the square. remains the same. is divided by 2. is doubled. is multiplied by 4 22. If the radius of a circle is doubled, then the circumference of the circle is multiplied by. 1 2. 2. 16. 4 27. If the ratio of the corresponding sides of two similar triangles is 3 : 5, the ratio of the areas of these triangles is. 3 : 5. 3 : 5 23. If the ratio of the edges of two cubes is 2 : 3, the ratio of the two volumes is. 9 : 25. 27: 125. 2 : 3. 4 : 9. 8 : 27. 2 : 5 28. If 5 is added to both the length and the width of a rectangle, then the perimeter is increased by 24. rectangle has an area of 20. If the length of the rectangle is doubled and the width remains the same, what is the area of the new rectangle?. 5. 10. 20. 25 page 5
29. If the ratio of the sides of two cubes is 3 : 4, what is the ratio of the volumes of the two cubes?. 3 : 4. 9 : 12. 9 : 16. 27: 64 32. The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?. 10%. 21%. 25%. 31% 30. If the length of a rectangular prism is doubled, its width is tripled, and its height remains the same, what is the volume of the new rectangular prism?. double the original volume. triple the original volume. six times the original volume. nine times the original volume 33. had had a garden that was in the shape of a rectangle. Its length was twice its width. He decided to make a new garden that was 2 feet longer and 2 feet wider than his first garden. If x represents the original width of the garden, which expression represents the difference between the area of his new garden and the area of the original garden?. 6x + 4. 2x 2 31. planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. The owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. What will be the new length of this building?. x 2 + 3x + 2. 8. 106 ft. 108 ft. 110 ft. 112 ft page 6
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