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

The volume of a sphere

Maths

In this unit, pupils have increased their knowledge of volume which is used in the compound measures unit as the formula for density involves volume. 

In the prior unit, pupils built upon their learning of the area of different shapes. In this unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

This lesson will be removed by end of Summer Term 2025.

The volume of a sphere

Lesson outcome

This lesson will be removed by end of Summer Term 2025.