E24.3 Scale drawings

Grade 7

Exercise 24.3

Scale drawings

By Ben Chen

A scale drawing lets you show something very large on a piece of paper.

Scale drawing

Multiple Choice

What is a scale drawing?

• It let's you climb something very tall

• It lets you weigh something very tall

• It lets you weigh something very large

• It lets you show something very large on a piece of paper

Worked example a)

A diagram is drawn to a scale of 1 : 25. A line on the diagram has length

20 cm. What actual length does it represent?

Solution to a)

A diagram is drawn to a scale of 1 : 25. A line on the diagram has length

20 cm. What actual length does it represent?

​1 : 25 means real life is 25 times bigger than the drawing.

20 × ​25 = 500

​So 20 cm on the diagram represents 500 cm (5 m) in real life.

Multiple Choice

A diagram is drawn to a scale of 1 : 50. A line on the diagram has length 40 cm. What actual length does it represent?

• 2 cm

• 20 cm

• 200 cm

• 2,000 cm

Multiple Choice

A diagram is drawn to a scale of 1 : 50. A line on the diagram has length 40 cm. What actual length does it represent?

• 0.2 m

• 2 m

• 20 m

• 200 m

Multiple Choice

A diagram is drawn to a scale of 1 : 100. The real life length is 80 cm.

What is the length of the line in the diagram?

• 0.8 cm

• 8 cm

• 80 cm

• 800 cm

Multiple Choice

A diagram is drawn to a scale of 1 : 10. The real life length is 90 m.

What is the length of the line in the diagram?

• 0.9 cm

• 9 cm

• 90 cm

• 900 cm

Worked example c)

A circular arena is being built. On a scale drawing, the radius of the arena is 8 cm. The radius of the actual arena is 120 m. Calculate the scale of the drawing.

Solution to c)

A circular arena is being built. On a scale drawing, the radius of the arena is 8 cm. The radius of the actual arena is 120 m. Calculate the scale of the drawing.

First, change the 120 m to cm.

120 m ×​ 100 cm/m = 12,000 cm

​Then, divide the real life length by the drawing length

12,000 cm ÷​ 8 cm = 1,500

Therefore, the scale ​of the drawing is 1 : 1,500

Multiple Choice

A circular arena is being built. On a scale drawing, the radius of the arena is 7 cm. The radius of the actual arena is 91 m. Calculate the scale of the drawing.

• 1 : 1,100

• 1 : 1,200

• 1 : 1,300

• 1 : 1,400