Volume of cones, spheres and pyramids

The Maths Habit

A cone and a cylinder are the same width and the same height.
How many cones full of water fill the cylinder?

3. The cone holds a third of the cylinder.

Work out

32 9

Same base, same height. How many cones of water fill the cylinder?

5 cm3 cm5 cm3 cm1 cone2 cones3 cones

The cylinder holds π × 32 × 5 cm³. How much does the cone hold?

Cylinder: π × 32 × 5 = 141.4 cm³

Cone: a third of it, 141.4 ÷ 3 = 47.1 cm³

Cone: V = 13πr2h

Same base, same height: 3 pyramids of water fill the cuboid. Find the volume of the pyramid.

4 cm3 cm5 cm

Cuboid: 4 × 3 × 5 = 60 cm³

Pyramid: 60 ÷ 3 = 20 cm³

Pyramid: V = 13 × base area × height

Cone: V = 13πr2h

Sphere: V = 43πr3

Pyramid: V = 13 × base area × height

A cone has radius 4 cm and height 6 cm. Find its volume to 1 decimal place.

6 cm4 cm
V =13× π ×42×6
Volume100.5 cm³

A cone has radius 2 cm and height 9 cm. Find its volume to 1 decimal place.

9 cm2 cm
V =13× π ×22×9
Volume37.7 cm³

A cone has radius 4 cm and height 6 cm. Find its volume to 1 decimal place.

6 cm4 cm
V =13× π ×42×6
Volume100.5 cm³

A cone has radius 5 cm and height 3 cm. Find its volume to 1 decimal place.

3 cm5 cm
V =13× π ×52×3
Volume78.5 cm³

A cone has radius 4 cm and height 6 cm. Find its volume to 1 decimal place.

6 cm4 cm
V =13× π ×42×6
Volume100.5 cm³

A cone has radius 6 cm and height 8 cm. Find its volume to 1 decimal place.

8 cm6 cm
V =13× π ×62×8
Volume301.6 cm³

A cone has radius 4 cm and height 6 cm. Find its volume to 1 decimal place.

6 cm4 cm
V =13× π ×42×6
Volume100.5 cm³

A sphere has radius 3 cm. Find its volume to 1 decimal place.

3 cm
V =43× π ×33
Volume113.1 cm³

A cone has radius 4 cm and height 6 cm. Find its volume to 1 decimal place.

6 cm4 cm
V =13× π ×42×6
Volume100.5 cm³

A pyramid has a square base of side 5 cm and a height of 12 cm. Find its volume.

12 cm5 cm
V =13×25×12
Volume100 cm³

A sphere has radius 7 cm. Find its volume to 1 decimal place.

7 cm
V =43× π ×73
Volume1,436.8 cm³

A sphere has radius 2.5 cm. Find its volume to 1 decimal place.

2.5 cm
V =43× π ×2.53
Volume65.4 cm³

A pyramid has a 6 cm by 2 cm rectangular base. Its volume is 28 cm³. Find its height.

6 cm2 cmh
28=13×12× h
Height28 × 3 ÷ 12 = 7 cm

A pyramid has a square base of side 4 cm. Its volume is 48 cm³. Find its height.

4 cm4 cmh
48=13×16× h
Height48 × 3 ÷ 16 = 9 cm

Volume of cones, spheres and pyramids worksheet, page 1

Answer sheet

  1. A cone and a cylinder have the same radius and the same height. How many cones of water fill the cylinder?

    3

  2. A sphere has diameter 12 cm. Find its volume to 1 decimal place.

    904.8 cm³

  3. A pyramid has a 5 cm by 3 cm base. Its volume is 50 cm³. Find its height.

    50 × 3 ÷ 15 = 10 cm

  4. A pyramid has a rectangular base 8 cm by 7 cm and a height of 9 cm. Find its volume.

    56 × 9 ÷ 3 = 168 cm³

  1. Find the volume of the cone to 1 decimal place.

    263.9 cm3
    7 cm6 cm

  2. Find the volume of the sphere to 1 decimal place.

    268.1 cm3
    4 cm

  3. A pyramid has a square base of side 6 cm. Its volume is 96 cm³. Find its height.

    8 cm
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