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Scale Drawings

What you'll learn

  • How to compare lengths on an accurate drawing.
  • How to use scales such as 1:50 and 1:50000.
  • How to change answers from centimetres into metres or kilometres.
  • How to estimate a perimeter from a scale drawing.

1. What is a scale drawing?

A scale drawing is a drawing that is the same shape as the real object, but a different size. It might show a car, a house, a field or a map.

A scale drawing keeps the same shape while making every length larger or smaller by the same multiplier.

An estimate is a sensible approximate answer. In these questions, you often estimate by measuring or comparing lengths on the drawing.

Definition

Scale drawing, scale and scale factor

  • A scale drawing is a drawing where all lengths have been enlarged or reduced by the same multiplier.

  • A scale tells you how a length on the drawing or model compares with the real length.

  • The scale factor is the multiplier used to get from the drawing or model to the real object.

Common Mistake

Only trust accurate drawings

Only measure or compare lengths when the question says the drawing is accurate or gives a scale. A rough sketch is not meant to be measured.

2. Comparing lengths on a drawing

Sometimes no written scale is given. Instead, you compare two lengths on the same drawing.

For example, if one height on the drawing is about 3 times another height, then the real height is also about 3 times as big.

Key Idea

Same multiplier

On an accurate scale drawing, matching lengths stay in the same proportion. If the drawing height doubles, the real height doubles too.

Example

Estimating a larger height

A scale drawing shows a small plant pot and a tall cupboard. The cupboard looks about 4 times as tall as the plant pot. The real plant pot is 25 cm tall. Estimate the real height of the cupboard.

The cupboard is compared with the plant pot using height with height, and is about four times as tall.

  1. Compare the matching lengths. We are comparing height with height.

  2. The cupboard is about 4 times the height of the plant pot.

  3. Multiply the real height of the plant pot by 4.

    25×4=10025 \times 4 = 10025×4=100

  4. The estimated real height of the cupboard is 100 cm.

Common Mistake

Comparing the wrong lengths

If you are given a real height, compare heights on the drawing. If you are given a real length, compare lengths. Do not compare a height with a width unless the question clearly tells you to.

3. When the drawing uses a fraction

Sometimes the drawing shows that one length is a fraction of another.

For example, if the height of a vehicle is about one third of its length, then its length is about 3 times its height.

Example

Finding a real length from a height

A scale drawing shows a van. The height of the van looks about one third of its length. The real height of the van is 1.8 m. Estimate the real length of the van.

The van’s height is about one third of its length, so the length is about three height sections.

  1. The height is about one third of the length.

  2. So the length is about 3 times the height.

  3. Multiply the real height by 3.

    1.8×3=5.41.8 \times 3 = 5.41.8×3=5.4

  4. The estimated real length of the van is 5.4 m.

Tip

Turn the fraction around

If the height is about one quarter of the length, then the length is about 4 times the height. If the height is about one third of the length, then the length is about 3 times the height.

4. Using a written scale

A written scale such as 1:50 means:

  • 1 cm on the drawing or model represents 50 cm in real life.
  • So to find the real length, multiply the model length by 50.

For a scale of 1:50000:

  • 1 cm on the map represents 50000 cm in real life.
  • So to find the real distance, multiply the map distance by 50000.
Example

Model length to real length

A model bus is 12 cm long. The scale of the model is 1:60. Work out the real length of the bus in metres.

The model bus length is scaled up by 60 to represent the real bus.

  1. The scale 1:60 means 1 cm on the model represents 60 cm in real life.

  2. Multiply the model length by 60 to get the real length in centimetres.

    12×60=72012 \times 60 = 72012×60=720

  3. Change 720 cm into metres by dividing by 100.

    720÷100=7.2720 \div 100 = 7.2720÷100=7.2

  4. The real bus is 7.2 m long.

Common Mistake

Mixing up the units

A scale like 1:60 uses the same units on both sides. It means 1 cm represents 60 cm, not 60 m.

5. Map scales and kilometres

A unit tells you what a measurement is in, such as cm, m or km.

Map distances are often measured in centimetres, but the final answer may need to be in kilometres.

Remember:

  • To change cm to m, divide by 100.
  • To change cm to km, divide by 100000.
Example

Map distance to real distance

On a map with scale 1:50000, two villages are 7 cm apart. Work out the real distance between them in kilometres.

The map distance between the villages is 7 cm, which is then converted using the map scale.

  1. The scale 1:50000 means 1 cm on the map represents 50000 cm in real life.

  2. Multiply 7 cm by 50000.

    7×50000=3500007 \times 50000 = 3500007×50000=350000

  3. The real distance is 350000 cm.

  4. Change centimetres to kilometres by dividing by 100000.

    350000÷100000=3.5350000 \div 100000 = 3.5350000÷100000=3.5

  5. The real distance is 3.5 km.

Tip

A quick map shortcut

For a scale of 1:50000, every 2 cm on the map is 1 km in real life, because 100000 cm is 1 km.

6. Perimeter from a scale drawing

The perimeter is the total distance around the outside of a shape.

For a rectangle, you add all four sides:

The perimeter of a rectangle is found by adding the two lengths and the two widths around the outside.

length + width + length + width.

If the drawing shows the length and width in the same scale, you can estimate one real side from the other, then add the sides.

Example

Estimating the perimeter of a field

A scale drawing shows a rectangular field. The real length of the field is 48 m. On the drawing, the width looks about half of the length. Estimate the real perimeter.

The field’s width is estimated as about half of its 48 m length before adding all four sides.

  1. The width is about half of the length.

  2. Find half of 48 m.

    48÷2=2448 \div 2 = 2448÷2=24

  3. So the estimated width is 24 m.

  4. Add all four sides of the rectangle.

    48+24+48+24=14448 + 24 + 48 + 24 = 14448+24+48+24=144

  5. The estimated perimeter is 144 m.

Exam technique

In the exam

  1. Check whether you are comparing lengths on a drawing or using a written scale.

  2. Keep units sensible: scale calculations usually start in cm, then convert to m or km if needed.

  3. For estimates, write an answer that matches the drawing reasonably; it does not need to be perfect.

Self review

Check yourself

  • If a model has scale 1:80, what does 1 cm on the model represent in real life?

  • Why must you compare height with height, not height with length?

  • How do you change a real distance in centimetres into kilometres?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

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Scale Drawings Revision Guide

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  2. /Maths
  3. /Scale Drawings