A map is a scale drawing.
Scale drawings are used in many jobs, by people such as designers, builders and engineers to show a plan of a larger object.
A scale drawing is the same shape but a different size as the original object.
A scale drawing has a scale which is a ratio showing how the size of the drawing is related to the true size of the object.
Scale = drawing length : true length
Ways of writing of scales
| As a ratio | 1 cm : 1 km |
| As an equation | 1 cm = 1 km |
| In words | 1 cm to 1 km |
Calculating Scales
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This is a drawing of the Stone Store at Keri Keri.
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This is a photograph of the Stone Store at Keri Keri. |
The drawing is about 3 cm long.
The real building is about 30 metres long.
So the scale is:
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3 cm : 30 m
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3 cm : 3000 cm |
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1 cm : 1000 cm | |
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1 : 1000 |
This means that the real building is 1000 times bigger than the scale drawing.
Notice that the ratio in a scale is usually written in its simplest form.
Maps
The scales given for maps are often calculated from a ratio with different units. These two examples use maps of Australia and New Zealand.
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The distance across Australia from a town on the west coast to Brisbane on the east coast is about 4050 km. The same distance measured on this map of Australia, when printed out, is about 9 cm. Therefore, the scale of this map is 9 cm : 4050 km = 1 cm : 450 km = 1 cm : 45 000 000 cm = 1 : 45 000 000 |
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The length of New Zealand from Cape Reinga at the north of the North Island to Bluff at the south of the South Island is about 1500 km. The same distance measured on this map of New Zealand, when printed out, is about 15 cm. Therefore, the scale of this map is 15 cm : 1500 km = 1 cm : 100 km = 1 cm : 10 000 000 cm = 1 : 10 000 000 |
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Examples of Scale Drawing Problems
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Example 1
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Example 2
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Example 3
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| Simplify the scale 5 mm : 100 cm |
The scale on a map is 1 : 1000. |
A bus is 20 metres long. On a plan with a scale of 1 : 100, how long would the bus be? |
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Answer
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Answer For a scale of 1 : 1000 1 cm on map is equivalent to 1000 cm 25 cm is equivalent to 25 × 1000 cm = 25 000 cm = 250 metres |
Answer For a scale of 1 : 100 1 metre on plan is equivalent to 100 metres. 1 ÷ 100 metres is equivalent to 1 metre 0.01 metres is equivalent to 1 metre 0.20 metres is equivalent to 20 metres. The bus would be 20 centimetres on the plan. |
