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

Checking and securing understanding of nets of solids

Checking and securing understanding of volume of prisms

Checking and securing understanding of surface area of cuboids

Checking and securing understanding of surface area of other prisms

Checking and securing understanding of volume of a cylinder

Checking and securing understanding of surface area of a cylinder

The surface area of a pyramid

The volume of a pyramid

The surface area of a sphere

The volume of a sphere

The surface area of a cone

The volume of a cone

Surface area of composite solids

Volume of a frustum of a cone

Surface area of a frustum of a cone

Forming equations involving complex shape calculations

Advanced problem solving with further surface area and volume

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.

In this unit, pupils will further develop their understanding of shapes by considering the 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.

Starter Quiz

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