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.

The effect of enlargement on the volume of a 3D shape

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

__________ is the amount of space 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 3. Work out the volume of the enlarged cuboid.

Shape A is a 3D shape. Shape A is enlarged by scale factor 3 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 15 cm². The volume of prism B is {{ }} cm³.

The transformation that causes a change in {{}} of the object is enlargement.

Rectangles A and B are similar. What is the area scale factor from A to B?

Shapes P and Q are similar. The perimeter of shape P is 18 cm and the perimeter of shape Q is 72 cm. The area scale factor from P to Q is {{}}.

Sectors E and F are similar. The area of sector E is 30π cm². What is the area of sector F? 

Sectors E and F are similar. The area of shape E is 24π cm² and the area of sector F is 150π cm². The radius of sector F is {{}} cm.

Triangles L and M are similar. The area of triangle M is 54 cm². What is the perimeter of triangle M?

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

The effect of enlargement on the volume of a 3D shape

Lesson outcome

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