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

Starter quiz

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

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

$\frac{1}{25}$

$\frac{1}{5}$

5

25 ✓

125
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 ______.

'16' ✓
Sectors E and F are similar. The area of sector E is 30π cm². What is the area of sector F?

36π cm²

42π cm²

60π cm²

90π cm²

120π cm² ✓
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.

'15' ✓
Triangles L and M are similar. The area of triangle M is 54 cm². What is the perimeter of triangle M?

30 cm

33 cm

36 cm ✓

42 cm

48 cm

Exit quiz

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

area

perimeter

volume ✓
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.

480 cm³

540 cm³

1080 cm³

1620 cm³ ✓
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?

$\sqrt 3$

$3$

$6$

$9$

$27$ ✓
Match each linear scale factor to correct the volume scale factor.

Linear scale factor: $2$

⇔

Volume scale factor: $8$ ✓

Linear scale factor: $4$

⇔

Volume scale factor: $64$ ✓

Linear scale factor: $5$

⇔

Volume scale factor: $125$ ✓

Linear scale factor: $10$

⇔

Linear scale factor: $1000$ ✓
Prism S and prism T are similar. What is the scale factor of enlargement from prism S to prism T?

$\frac {3}{2}$

$\frac {9}{4}$

$\frac {4}{9}$

$\frac {8}{27}$

$\frac {27}{8}$ ✓
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.

'1440' ✓

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Lesson Details

Key learning points

An enlargement means the object and image are similar.
All lengths in the object have been multiplied by the scale factor.
Using index laws, this means the volume has been multiplied by the scale factor cubed.

Common misconception

I will get different linear scale factors if a measure corresponding lengths in cm vs inches.

Scale factors do not have dimensions, and aren't linked to specific units. If one length is 23 cm (9 inches), and a corresponding length is 69 cm (27 inches), then the scale factor between them is 3, regardless of whether we measured in cm or inches.

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.