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

The surface area 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)

Complete the formula for the surface area of a sphere, with a radius of $$r$$: surface area = {{}}$$\pi r^2$$.

A sphere has a surface area of 196𝜋 m². The radius of the sphere is {{ }} m.

The radius of this hemisphere is 6 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 192𝜋 cm². The radius of the hemisphere is {{ }} cm.

Match each letter to the name of the shape.

Surface area = $$2 \pi \times 2 + \pi  \times 2 \times 9^2$$

Surface area = $$ \pi \times 2^2 + 2\pi \times 2 \times 9$$

Surface area = $$2 \pi \times 2^2 + 2\pi  \times 2 \times 9$$

Surface area = $$ 2\pi  \times 2 \times 9$$

Surface area = $$\pi \times 2^2 + 2\pi  \times 2^2 \times 9$$

Which calculation gives the surface area of a cylinder of radius 2 cm and height 9 cm?

The area of a circle is 19.6 cm². What is the radius of the circle? Give your answer correct to 1 decimal place.

A cylinder has a radius of 3 mm and a height of 10 mm. The volume of the cylinder, in terms of $$\pi$$, is {{}}$$\pi $$ mm³.

A cylinder has a radius of 3 mm and a height of 10 mm. The surface area of the cylinder, in terms of $$\pi$$, is {{}}$$\pi $$ mm².

The volume of a cube is 125 cm³. The surface area of the cube is {{}} cm².

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

The surface area of a sphere

Lesson outcome

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