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The volume of a sphere

I can calculate the volume of a sphere.

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Lesson 10 of 18

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Year 11

The volume of a sphere

I can calculate the volume of a sphere.

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Key learning points

The volume of a sphere can be found by displacement.
Putting a sphere into a cylinder filled with water displaces the water.
When the sphere is removed, the water level drops.
The volume of the sphere is the difference between the volume of the cylinder and water.
There is a formula you can use to calculate the volume of a sphere.

Keywords

Sphere - A sphere is a 3D shape, where every point on its surface is equidistant from the centre.

Common misconception

Pupils may multiply the radius of the sphere by the constant before cubing it.

Remind pupils of the order of operations and the need to cube the radius before multiplying by the constants in the formula.

This topic could be linked to volume scale factors to increase the challenge.

Teacher tip

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
A is a 3D shape, where every point on its surface is equidistant from the centre.

Correct Answer: sphere

Q2.
Which of the following calculates the surface area of a sphere, with a radius of $$r$$?

$$4 \pi r$$

Correct answer: $$4 \pi r^2$$

$$4 \pi r^3$$

$$2\pi r^2$$

$$2\pi r^3$$

Q3.
Match each sphere to its surface area.

Correct Answer:Diameter of sphere = 10 cm,100𝜋

Correct Answer:Radius of sphere = 4 cm,64𝜋

Correct Answer:Radius of sphere = 3 cm,36𝜋

Correct Answer:Diameter of sphere = 1 cm,𝜋

Correct Answer:Radius of sphere = 2 cm,16𝜋

Correct Answer:Diameter of sphere = 2 cm,4𝜋

Q4.
A sphere has a surface area of 9𝜋 m². The radius of the sphere is m.

Correct Answer: 1.5, 3/2

Q5.
The radius of this hemisphere is 20 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

1260 cm²

2510 cm²

Correct answer: 3770 cm²

5030 cm²

Q6.
The total surface area of this hemisphere is 432𝜋 cm². The radius of the hemisphere is cm.

Correct Answer: 12, 12 cm, 12cm

Assessment exit quiz

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6 Questions

Q1.
A sphere is a 3D shape, where every point on its surface is from the centre.

Correct Answer: equidistant, equi-distant, equal distance

Q2.
Work out the volume of a sphere with radius 2.5 m. Give your answer correct to 1 decimal place.

19.6 m³

20.8 m³

26.2 m³

49.1 m³

Correct answer: 65.4 m³

Q3.
A sphere has a radius of 6 mm. The volume of the sphere, in terms of 𝜋, is 𝜋 mm³.

Correct Answer: 288

Q4.
Which of these calculations finds the volume of a hemisphere with a radius of 12 cm?

Correct answer: $$ \frac{2}{3} \times \pi \times 12^3 $$

$$ \frac{2}{6} \times \pi \times 12^3 $$

$$ \frac{4}{3} \times \pi \times 6^3 \div 2$$

Correct answer: $$ \frac{1}{2} \times \frac{4}{3} \times \pi \times 12^3$$

$$ \frac{4}{3} \times \pi \times 8^3 \div 2$$

Q5.
The volume of a hemisphere with a radius of 12 cm, in terms of $$\pi$$, is $$\pi$$ cm³.

Correct Answer: 1152

Q6.
The volume of a hemisphere is 144𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is 𝜋 cm².

Correct Answer: 108

Lesson appears in

UnitMaths / 2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Maths

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The volume of a sphere

The volume of a sphere

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.A is a 3D shape, where every point on its surface is equidistant from the centre.

Q2.Which of the following calculates the surface area of a sphere, with a radius of $$r$$?

Q3.Match each sphere to its surface area.

Q4.A sphere has a surface area of 9𝜋 m². The radius of the sphere is m.

Q5.The radius of this hemisphere is 20 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

Q6.The total surface area of this hemisphere is 432𝜋 cm². The radius of the hemisphere is cm.

Assessment exit quiz

6 Questions

Q1.A sphere is a 3D shape, where every point on its surface is from the centre.

Q2.Work out the volume of a sphere with radius 2.5 m. Give your answer correct to 1 decimal place.

Q3.A sphere has a radius of 6 mm. The volume of the sphere, in terms of 𝜋, is 𝜋 mm³.

Q4.Which of these calculations finds the volume of a hemisphere with a radius of 12 cm?

Q5.The volume of a hemisphere with a radius of 12 cm, in terms of $$\pi$$, is $$\pi$$ cm³.

Q6.The volume of a hemisphere is 144𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is 𝜋 cm².

Lesson appears in

UnitMaths / 2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Maths

Q1.
A is a 3D shape, where every point on its surface is equidistant from the centre.

Q2.
Which of the following calculates the surface area of a sphere, with a radius of $$r$$?

Q3.
Match each sphere to its surface area.

Q4.
A sphere has a surface area of 9𝜋 m². The radius of the sphere is m.

Q5.
The radius of this hemisphere is 20 cm. Work out the total surface area of the hemisphere. Give your answer correct to 3 significant figures.

Q6.
The total surface area of this hemisphere is 432𝜋 cm². The radius of the hemisphere is cm.

Q1.
A sphere is a 3D shape, where every point on its surface is from the centre.

Q2.
Work out the volume of a sphere with radius 2.5 m. Give your answer correct to 1 decimal place.

Q3.
A sphere has a radius of 6 mm. The volume of the sphere, in terms of 𝜋, is 𝜋 mm³.

Q4.
Which of these calculations finds the volume of a hemisphere with a radius of 12 cm?

Q5.
The volume of a hemisphere with a radius of 12 cm, in terms of $$\pi$$, is $$\pi$$ cm³.

Q6.
The volume of a hemisphere is 144𝜋 cm³. The surface area of the hemisphere, in terms of 𝜋, is 𝜋 cm².