Volume practice questions

Volume questions

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1. 1VolumeFoundation

   A cube has side length 3. Enter its volume.A cube has side length 3. Enter its volume.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 2727

   Volume of a cube is the side cubed: 3³ = 27. Its surface area is 6(3²) = 54, which answers a different question and is the commonest wrong choice here.Volume of a cube is the side cubed: 3^3 = 27. Its surface area is 6(3^2) = 54, which answers a different question and is the commonest wrong choice here.

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2. 2VolumeFoundation

   A rectangular box measures 5 by 4 by 3 centimeters. Enter its volume in cubic centimeters.A rectangular box measures 5 by 4 by 3 centimeters. Enter its volume in cubic centimeters.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 6060

   Volume is length times width times height: 5 × 4 × 3 = 60 cubic centimeters.Volume is length times width times height: 5 × 4 × 3 = 60 cubic centimeters.

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3. 3VolumeStandard

   A cylinder has radius 2 and height 5. What is its volume in terms of π?A cylinder has radius 2 and height 5. What is its volume in terms of π?

   • A25π25π
   • B10π10π
   • C20π20π
   • D40π40π
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   Answer: 20π20π

   Cylinder volume is π r² h: π(2²)(5) = 20π. Square the radius before multiplying by the height — doubling instead of squaring gives 20π by luck here, but not generally.Cylinder volume is π r^2 h: π(2^2)(5) = 20π. Square the radius before multiplying by the height — doubling instead of squaring gives 20π by luck here, but not generally.

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4. 4VolumeStandard

   A cone has radius 3 and height 4. What is its volume in terms of π?A cone has radius 3 and height 4. What is its volume in terms of π?

   • A9π9π
   • B16π16π
   • C12π12π
   • D36π36π
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   Answer: 12π12π

   The volume of a cone is (13)π r² h. With r = 3 and h = 4, that is (13)(9)(4)π = 12π, which is one third of the cylinder with the same base and height.The volume of a cone is (1/3)π r^2 h. With r = 3 and h = 4, that is (1/3)(9)(4)π = 12π, which is one third of the cylinder with the same base and height.

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5. 5VolumeStandard

   A rectangular tank measures 4 by 3 by 2 meters. If its height is doubled and the other dimensions are unchanged, what happens to its volume?A rectangular tank measures 4 by 3 by 2 meters. If its height is doubled and the other dimensions are unchanged, what happens to its volume?

   • AIt increases by 8 times.It increases by 8 times.
   • BIt doubles.It doubles.
   • CIt quadruples.It quadruples.
   • DIt is unchanged.It is unchanged.
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   Answer: It doubles.It doubles.

   Volume is length times width times height. Scaling only one dimension by 2 multiplies the volume by 2. Doubling all three would multiply it by 8.Volume is length times width times height. Scaling only one dimension by 2 multiplies the volume by 2. Doubling all three would multiply it by 8.

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6. 6VolumeStandard

   A cylinder has volume 100π and height 4. What is its radius?A cylinder has volume 100π and height 4. What is its radius?

   • A2525
   • B55
   • C1010
   • D6.256.25
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   Answer: 55

   From π r² h = 100π with h = 4: r² = 25, so r = 5. Stopping at 25 skips the square root.From π r^2 h = 100π with h = 4: r^2 = 25, so r = 5. Stopping at 25 skips the square root.

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7. 7VolumeStandard

   A cylinder has radius 5 cm and height 12 cm. What is its volume, in terms of π?A cylinder has radius 5 cm and height 12 cm. What is its volume, in terms of π?

   • A300π cubic cm300π cubic cm
   • B120π cubic cm120π cubic cm
   • C60π cubic cm60π cubic cm
   • D900π cubic cm900π cubic cm
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   Answer: 300π cubic cm300π cubic cm

   Volume is π r² h = π(25)(12) = 300π cubic cm. Using r rather than r² gives 60π, and doubling the radius before squaring gives 900π.Volume is π r^2 h = π(25)(12) = 300π cubic cm. Using r rather than r^2 gives 60π, and doubling the radius before squaring gives 900π.

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8. 8VolumeStandard

   A cube has a volume of 343 cubic centimeters. Enter the length of one edge, in centimeters.A cube has a volume of 343 cubic centimeters. Enter the length of one edge, in centimeters.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 77

   The volume of a cube is the edge cubed, so the edge is the cube root of 343, which is 7 because 7 × 7 × 7 = 343.The volume of a cube is the edge cubed, so the edge is the cube root of 343, which is 7 because 7 × 7 × 7 = 343.

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9. 9VolumeStandard

   A rectangular prism measures 4 cm by 5 cm by 9 cm. What is its volume?A rectangular prism measures 4 cm by 5 cm by 9 cm. What is its volume?

   • A18 cubic cm18 cubic cm
   • B90 cubic cm90 cubic cm
   • C180 cubic cm180 cubic cm
   • D360 cubic cm360 cubic cm
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   Answer: 180 cubic cm180 cubic cm

   Volume is the product of the three dimensions: 4 × 5 × 9 = 180 cubic cm. The choice 18 adds them instead, and 90 multiplies only two.Volume is the product of the three dimensions: 4 × 5 × 9 = 180 cubic cm. The choice 18 adds them instead, and 90 multiplies only two.

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10. 10VolumeStandard

    A cone has a radius of 3 cm and a height of 7 cm. What is its volume, in terms of π?A cone has a radius of 3 cm and a height of 7 cm. What is its volume, in terms of π?

    • A63π cubic cm63π cubic cm
    • B21π cubic cm21π cubic cm
    • C7π cubic cm7π cubic cm
    • D9π cubic cm9π cubic cm
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    Answer: 21π cubic cm21π cubic cm

    The volume of a cone is one third of π r² h: (13)(π)(9)(7) = 21π cubic cm. Omitting the one third gives 63π, which is the cylinder the cone sits inside.The volume of a cone is one third of π r^2 h: (1/3)(π)(9)(7) = 21π cubic cm. Omitting the one third gives 63π, which is the cylinder the cone sits inside.

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11. 11VolumeStandard

    A cylinder has a radius of 6 and a height of 4. What is its volume, in terms of π?A cylinder has a radius of 6 and a height of 4. What is its volume, in terms of π?

    • A48π48π
    • B144π144π
    • C96π96π
    • D576π576π
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    Answer: 144π144π

    Volume is π r² h = π(36)(4) = 144π. Using r rather than r² gives 24π, and doubling the radius before squaring gives 576π.Volume is π r^2 h = π(36)(4) = 144π. Using r rather than r^2 gives 24π, and doubling the radius before squaring gives 576π.

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12. 12VolumeChallenge

    A sphere has radius 3. What is its volume in terms of π?A sphere has radius 3. What is its volume in terms of π?

    • A36π36π
    • B12π12π
    • C108π108π
    • D27π27π
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    Answer: 36π36π

    The volume of a sphere is (43)π r³. With r = 3, r³ = 27, so the volume is (43)(27)π = 36π.The volume of a sphere is (4/3)π r^3. With r = 3, r^3 = 27, so the volume is (4/3)(27)π = 36π.

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13. 13VolumeChallenge

    A cylinder and a cone have the same radius and the same height. Enter the number of cone-fulls needed to fill the cylinder.A cylinder and a cone have the same radius and the same height. Enter the number of cone-fulls needed to fill the cylinder.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 33

    A cone's volume is one third of the cylinder with the same base and height, so three cone-fulls fill it.A cone's volume is one third of the cylinder with the same base and height, so three cone-fulls fill it.

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