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

A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.

Volume of composite solids

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)

The amount of space occupied by a closed 3D shape is called the {{}} of the shape.

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 12 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 8 cm.  The volume of the solid is {{ }}cm³ (correct to 3 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.

A shape created using two or more basic shapes is called a {{}} shape.

This composite solid is constructed from two cuboids. All lengths given are in centimetres. Calculate the total surface area of the solid.

This composite solid is constructed from two congruent cuboids. All lengths given are in centimetres. The total surface area of the solid is {{ }} cm².

The composite solid is constructed by placing a hemisphere with diameter 8 cm on top of a cuboid. Find the surface area of the solid. 

The composite solid is constructed with a cylinder and a hemisphere. Each have a diameter of 12 cm.  Find the surface area of the solid. 

The composite solid is constructed with a cone and a hemisphere. The surface area, in terms of 𝜋, is {{ }}𝜋 cm².

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

Volume of composite solids

Lesson outcome

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