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Volume of cylinders, cones and spheres worksheet

Grade 8 math, Common Core 8.G.C.9. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Volume of cylinders, cones and spheres

Grade 8 math, Common Core 8.G.C.9

Find each volume. Use 3.14 for π and round to the nearest tenth, or leave the answer in terms of π when asked.

  1. 1.
    A sphere has a radius of 6 ft. Leave the answer in terms of π.
  2. 2.
    A ball has a diameter of 14 cm. Find its volume.
  3. 3.
    A cylinder has a radius of 7 cm and a height of 5 cm.
  4. 4.
    A cylinder has a radius of 3 in and a height of 3 in.
  5. 5.
    A cone has a radius of 7 in and a height of 3 in. Leave the answer in terms of π.
  6. 6.
    A cone has a radius of 6 in and a height of 12 in. Leave the answer in terms of π.
  7. 7.
    A sphere has a radius of 3 ft. Leave the answer in terms of π.
  8. 8.
    A cylinder has a volume of 27π ft³ and a radius of 3 ft. How tall is it?
  9. 9.
    A ball has a diameter of 10 m. Find its volume.
  10. 10.
    A sphere has a radius of 6 in. Leave the answer in terms of π.
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Volume of cylinders, cones and spheres

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 288π ft³

    V = 43 × π × 6³ = 43 × 216π = 288π

  2. 2. ≈ 1,436.0 cm³

    r = 7V = 43 × 3.14 × 7³ ≈ 1,436.0

  3. 3. ≈ 769.3 cm³

    V = 3.14 × 7² × 5 = 3.14 × 245

  4. 4. ≈ 84.8 in³

    V = 3.14 × 3² × 3 = 3.14 × 27

  5. 5. 49π in³

    V = 13 × π × 7² × 3 = 49π

  6. 6. 144π in³

    V = 13 × π × 6² × 12 = 144π

  7. 7. 36π ft³

    V = 43 × π × 3³ = 43 × 27π = 36π

  8. 8. 3 ft

    π × 3² × h = 27πh = 27 ÷ 9 = 3

  9. 9. ≈ 523.3 m³

    r = 5V = 43 × 3.14 × 5³ ≈ 523.3

  10. 10. 288π in³

    V = 43 × π × 6³ = 43 × 216π = 288π

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About volume of cylinders, cones and spheres

Cylinder: V = πr²h, the area of the circle base times the height. Cone: V = 13πr²h, exactly a third of the cylinder with the same base and height. Sphere: V = 43πr³. Volume is in cubic units.

Worked example 1

A ball has a diameter of 8 m. Find its volume.
  1. Step 1.r = 4
  2. Step 2.V = 43 × 3.14 × 4³ ≈ 267.9

Answer: ≈ 267.9 m³

Worked example 2

A cylinder has a volume of 11π ft³ and a radius of 1 ft. How tall is it?
  1. Step 1.π × 1² × h = 11π
  2. Step 2.h = 11 ÷ 1 = 11

Answer: 11 ft

Worked example 3

A sphere has a radius of 9 cm. Leave the answer in terms of π.
  1. Step 1.V = 43 × π × 9³ = 43 × 729π = 972π

Answer: 972π cm³

Watch out for

  • Use the radius, not the diameter. Halve the diameter first.
  • A cone is one third of a cylinder with the same base and height.
  • Leaving the answer “in terms of π” means writing it like 36π, without multiplying by 3.14.

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On StudyWiz, your kid can practice volume of cylinders, cones and spheres with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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