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

Checking and securing understanding of direct proportion in context

The effect of enlargement on the perimeter of a shape

The effect of enlargement on the area of a shape

Using the scale factor for enlarging an area

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

Checking and securing understanding of congruent triangles (SSS)

Checking and securing understanding of congruent triangles (SAS)

Checking and securing understanding of congruent triangles (ASA)

Checking and securing understanding of congruent triangles (RHS)

Problem solving with advanced similarity knowledge

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.

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.

Starter Quiz

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