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⏰ 8th grade math · Measure, Time & Money

Cylinders, cones and spheres

A cylinder's volume is the area of the circle at the bottom times the height: V = π r² h. Radius 3 and height 5: V = π × 3² × 5 = 45π cubic units. Leave the π in the answer.

Worked example

A cylinder has a radius of 3 ft and a height of 6 ft. What is its volume in terms of π?
V = πr²h
r = 3 fth = 6 ft
Answer: 54 π cubic ft
Use V = πr²h. V = π × 3² × 6 = 54π. In terms of π that is 54π cubic ft.

For grown-ups: Volume of cylinders, cones, spheres. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.G.C.9
What this practises, for teachers

Practices volume of cylinders, cones, spheres (8.G.C.9). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

Try three

  1. A cylinder has a radius of 1 cm and a height of 9 cm. What is its volume in terms of π?
    V = πr²h
    r = 1 cmh = 9 cm
    Show the answer and how
    Answer: 9 π cubic cm
    Use V = πr²h. V = π × 1² × 9 = 9π. In terms of π that is 9π cubic cm.
  2. A cylinder has a radius of 5 ft and a height of 4 ft. What is its volume in terms of π?
    V = πr²h
    r = 5 fth = 4 ft
    Show the answer and how
    Answer: 100 π cubic ft
    Use V = πr²h. V = π × 5² × 4 = 100π. In terms of π that is 100π cubic ft.
  3. A cylinder has a diameter of 8 m and a height of 11 m. What is its volume in terms of π?
    V = πr²h
    d = 8 mh = 11 m
    Show the answer and how
    Answer: 176 π cubic m
    The diameter is 8, so the radius is half of it: 4. Use V = πr²h. V = π × 4² × 11 = 176π. In terms of π that is 176π cubic m.

Before and after

Learn first: Circles: around and inside (7th)

Name: ____________________Date: ____________Score: ____ / 12

Cylinders, cones and spheres (8th grade)

  1. A cylinder has a radius of 5 m and a height of 7 m. What is its volume in terms of π?
    V = πr²h
    r = 5 mh = 7 m
  2. A cylinder has a radius of 3 cm and a height of 8 cm. What is its volume in terms of π?
    V = πr²h
    r = 3 cmh = 8 cm
  3. A cylinder has a radius of 3 in and a height of 4 in. What is its volume in terms of π?
    V = πr²h
    r = 3 inh = 4 in
  4. A cylinder has a radius of 2 ft and a height of 6 ft. What is its volume in terms of π?
    V = πr²h
    r = 2 fth = 6 ft
  5. A cylinder has a radius of 3 ft and a height of 7 ft. What is its volume in terms of π?
    V = πr²h
    r = 3 fth = 7 ft
  6. A cylinder has a radius of 1 in and a height of 2 in. What is its volume in terms of π?
    V = πr²h
    r = 1 inh = 2 in
  7. A cylinder has a radius of 1 in and a height of 6 in. What is its volume in terms of π?
    V = πr²h
    r = 1 inh = 6 in
  8. A cylinder has a radius of 6 ft and a height of 3 ft. Use 3.14 for π. What is its volume, rounded to the nearest tenth?
    V = πr²h
    r = 6 fth = 3 ft
  9. A cylinder has a diameter of 10 cm and a height of 7 cm. What is its volume in terms of π?
    V = πr²h
    d = 10 cmh = 7 cm
  10. A cylinder has a diameter of 16 in and a height of 13 in. What is its volume in terms of π?
    V = πr²h
    d = 16 inh = 13 in
  11. A cylinder has a radius of 4 m and a height of 8 m. Use 3.14 for π. What is its volume, rounded to the nearest tenth?
    V = πr²h
    r = 4 mh = 8 m
  12. A cylinder has a diameter of 8 ft and a height of 14 ft. Use 3.14 for π. What is its volume, rounded to the nearest tenth?
    V = πr²h
    d = 8 fth = 14 ft

Answer key

  1. 175 π cubic m
  2. 72 π cubic cm
  3. 36 π cubic in
  4. 24 π cubic ft
  5. 63 π cubic ft
  6. 2 π cubic in
  7. 6 π cubic in
  8. 339.1 cubic ft
  9. 175 π cubic cm
  10. 832 π cubic in
  11. 401.9 cubic m
  12. 703.4 cubic ft

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