Using the scale factor for enlarging a volume | Maths

Starter quiz

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

'space' ✓
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.

120 cm³

240 cm³

360 cm³

480 cm³ ✓

600 cm³
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?

$\sqrt5$

$5$

$15$

$25$

$125$ ✓
Match each linear scale factor to correct the volume scale factor.

Linear scale factor: $3$

⇔

Volume scale factor: $27$ ✓

Linear scale factor: $10$

⇔

Volume scale factor: $1000$ ✓

Linear scale factor: $2$

⇔

Volume scale factor: $8$ ✓

Linear scale factor: $6$

⇔

Volume scale factor: $216$ ✓

Linear scale factor: $9$

⇔

Volume scale factor: $729$ ✓
Prism S and prism T are similar. What is the scale factor of enlargement from prism S to prism T?

$\frac {4}{5}$

$\frac {5}{4}$

$\frac {15}{12}$

$\frac {25}{16}$

$\frac {125}{64}$ ✓
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.

'6480' ✓

Exit quiz

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

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

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 $k^3$ ✓
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 ______.

'9' ✓
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 ______.

'81' ✓
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.

240 cm³

460 cm³

720 cm³

960 cm³ ✓

1080 cm³
Cuboid A and cuboid B are similar. The volume of cuboid B is 405 cm³. The surface area of B is ______ cm².

'355.5' ✓

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Lesson Details

Key learning points

You can calculate the scale factor from the two volumes.
Having calculated the scale factor, you can find missing lengths.

Common misconception

A linear scale factor can only be found by finding the multiplicative relationship between two corresponding lengths.

A linear scale factor can also be found by cube rooting a volume scale factor, where the volume scale factor is found from the multiplicative relationship between the volumes of two similar 3D shapes.

Keywords

Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.
Enlargement - Enlargement is a transformation that causes a change of size.
Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Volume - Volume is the amount of space occupied by a closed 3D shape.