A frustum is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.

Volume is the amount of space occupied by a closed 3D shape.

Volume of a frustum of a cone

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 {{ }} is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.

The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.

The diagram shows a side elevation of a frustum. Find the volume of the large cone that the frustum is cut from. Give your answer correct to 3 significant figures.

The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.

A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 9 cm. The height of the small cone is {{ }} cm.

A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 9 cm. The volume of the frustum is {{ }}𝜋 cm

A {{}} solid can be decomposed to make the volume easier to calculate.

The diagram shows a composite solid constructed from two congruent cuboids. All lengths given are in centimetres. Which of these calculations give the total volume of the solid?

This composite solid is constructed from two cuboids. All lengths given are in metres. The total volume of the solid is {{ }} m³.

This composite solid is constructed by placing a hemisphere with diameter 10 cm on top of a cuboid. Find the volume of the solid. Give your answer to the nearest cubic centimetre.

This composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 12 cm. The volume of the solid is {{ }}cm³ (correct to 4 significant figures).

This composite solid is constructed with a cone and a hemisphere. The volume of the solid, in terms of 𝜋, is {{ }}𝜋 cm³.

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

Volume of a frustum of a cone

Lesson outcome

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