Area and volume scale factors

The Maths Habit

  1. Two similar rectangles: the small one is 4 cm by 6 cm. The large one is 10 cm wide. How long is it?

    15 cm

  2. Two similar triangles have matching sides of 9 cm and 3 cm. Another side of the large triangle is 12 cm. Find the matching side of the small one.

    4 cm

  3. Two similar cylinders are 8 cm and 20 cm tall. The small one has a radius of 3 cm. Find the radius of the large one.

    7.5 cm

A rug is twice as long and
twice as wide as a mat.
The mat costs £5. What is a
fair price for the rug?

£10 looks fair, but…

The rug has 4 times as much material, so £20

The small square is enlarged. How many small squares fit in the big square?

lengths × 2
lengths × 3

Lengths × 2: 2 × 2 = 4 squares

Lengths × 3: 3 × 3 = 9 squares

The lengths are multiplied by 2. How many times bigger is the area?

area 6 squares
lengths × 2

6 squares become 24 squares: 4 times the area, and 4 = 2²

Each length is multiplied by 2. How many small cubes make the big cube?

1 cube
lengths × 2

2 × 2 × 2 = 8 cubes

Length scale factor: k

Area scale factor: k2

Volume scale factor: k3

What is the area scale factor?

Length scale factor 3 9

What is the volume scale factor?

Length scale factor 2 8

Lengths 4 cm and 8 cm. The small area is 6 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer24 cm2

Lengths 2 cm and 6 cm. The small volume is 5 cm3. Find the large volume.

length scale factor3volume scale factor: cube it27
Answer135 cm3

Lengths 4 cm and 8 cm. The small area is 6 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer24 cm2

Lengths 5 cm and 10 cm. The small area is 9 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer36 cm2

Lengths 4 cm and 8 cm. The small area is 6 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer24 cm2

Lengths 4 cm and 12 cm. The small volume is 2 cm3. Find the large volume.

length scale factor3volume scale factor: cube it27
Answer54 cm3

Lengths 4 cm and 8 cm. The small area is 6 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer24 cm2

Lengths 3 cm and 15 cm. The small area is 4 cm2. Find the large area.

length scale factor5area scale factor: square it25
Answer100 cm2

Lengths 4 cm and 8 cm. The small area is 6 cm2. Find the large area.

length scale factor2area scale factor: square it4
Answer24 cm2

Lengths 7 cm and 14 cm. The small volume is 6 cm3. Find the large volume.

length scale factor2volume scale factor: cube it8
Answer48 cm3

Area and volume scale factors worksheet, page 1

Answer sheet

  1. A model car is built to a scale of 1 : 10. The model needs 5 ml of paint. How much paint does the real car need?

    500 ml

  2. Two similar jugs hold 250 ml and 2 litres. The small one is 9 cm tall. How tall is the large one?

    18 cm

  1. Two similar shapes have lengths 5 cm and 15 cm.
    The smaller has an area of 4 cm².
    Find the area of the larger.

    36 cm2

  2. Two similar solids have lengths 4 cm and 8 cm. The smaller has a volume of 7 cm³. Find the volume of the larger.

    56 cm3

  3. Two similar solids have volumes 5 cm³ and 135 cm³. The smaller is 3 cm tall. Find the height of the larger.

    9 cm
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