Two shapes are similar if the only difference between                        them is their size. Their side lengths are in the same proportions.

A property of a shape is invariant if that property has not changed after the shape is transformed.

Enlargement is a transformation that causes a change of size.

A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

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

Using the scale factor for enlarging a volume

Maths

In the prior unit, pupils enhanced their understanding of enlargement. In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

Similarity

A scale factor is the multiplier between {{}} shapes that describes how large one shape is compared to the other. 

The multiplier between their surface areas is $$2k$$

The multiplier between their surface areas is $$k^2$$

The multiplier between their volumes is $$3k$$

The multiplier between their volumes is $$k^3$$

The multiplier between corresponding edge lengths on a pair of similar objects is $$k$$. Select the correct statements.

Shapes X and Y are similar to each other. The volume of shape Y is 729 times larger than the volume of shape X. The linear scale factor from X to Y is {{ }}.

Shapes X and Y are similar. The volume of shape Y is 729 times larger than the volume of shape X. The area scale factor from X to Y is {{ }}.

Pyramid A and pyramid B are similar. The surface area of pyramid A is 50 cm² and its volume is 120 cm³. The surface area of pyramid B is 200 cm². Calculate the volume of pyramid B.

Cuboid A and cuboid B are similar. The volume of cuboid B is 405 cm³. The surface area of B is {{ }} cm².

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

A cuboid of dimensions 2 cm by 3 cm by 10 cm is enlarged by a scale factor of 2. Work out the volume of the enlarged cuboid.

Shape A is a 3D shape. Shape A is enlarged by scale factor 5 to give shape B. What is the volume scale factor from A to B?

Match each linear scale factor to correct the volume scale factor.

Prism S and prism T are similar. What is the scale factor of enlargement from prism S to prism T?

Prism A and prism B are similar. The end face of prism A has an area of 20 cm². The volume of prism B is {{ }} cm³.

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

Using the scale factor for enlarging a volume

Lesson outcome

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