Volume of Cones, Cylinders, and Spheres Quiz

Grade 8 · Math · Quiz

Test your ability to calculate and compare volumes of 3D curved figures.

Questions

1. Volume of a cylinder with radius 5 cm and height 4 cm? (pi = 3.14)

   1. 62.8 cm^3
   2. 125.6 cm^3
   3. 251.2 cm^3
   4. 314 cm^3
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   Answer: 314 cm^3

   V = pi x 25 x 4 = 100 x 3.14 = 314 cm^3.

2. A sphere with radius 2 in has greater volume than a cylinder with radius 2 in and height 2 in.

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   Answer: True

   V_sphere = (4/3) x pi x 8 = 33.5 in^3; V_cylinder = pi x 4 x 2 = 25.1 in^3. Sphere is larger.

3. The volume of a cone equals one-___ of a cylinder with the same base and height.

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   Answer: third

   V_cone = (1/3) x pi x r^2 x h — exactly one-third of the matching cylinder.

4. Sphere with radius 6 cm. Volume? (pi = 3.14)

   1. 150.7 cm^3
   2. 452.2 cm^3
   3. 904.3 cm^3
   4. 1206.4 cm^3
   Show answer

   Answer: 904.3 cm^3

   V = (4/3) x 3.14 x 216 = (4/3) x 678.24 = 904.3 cm^3.

5. Cone with height 12 and radius 5. Volume? (pi = 3.14)

   1. 94.2
   2. 314
   3. 628
   4. 942
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   Answer: 314

   V = (1/3) x 3.14 x 25 x 12 = (1/3) x 942 = 314.

6. Doubling the radius of a sphere doubles its volume.

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   Answer: False

   Doubling r multiplies volume by 2^3 = 8, not 2, since r is cubed in the formula.

7. Volume is always measured in ___ units.

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   Answer: cubic

   Volume is 3-dimensional so units are cubed: cm^3, m^3, in^3.

8. Cylindrical tank: radius 3 m, height 10 m. Capacity in m^3? (pi = 3.14)

   1. 94.2 m^3
   2. 188.4 m^3
   3. 282.6 m^3
   4. 942 m^3
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   Answer: 282.6 m^3

   V = pi x 9 x 10 = 90 x 3.14 = 282.6 m^3.

9. Which has the smallest volume with r=4 cm and h=6 cm where applicable?

   1. Cylinder
   2. Cone
   3. Sphere (r=4)
   4. All equal
   Show answer

   Answer: Cone

   V_cone = (1/3) x pi x 16 x 6 = 100.5; V_cylinder = pi x 16 x 6 = 301.4; V_sphere = (4/3) x pi x 64 = 268.1. Cone is smallest.

10. The volume of a sphere with radius 3 equals 36 times pi.

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    Answer: True

    V = (4/3) x pi x 27 = 36 x pi. Exact answer.

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