Unit 19 Section 3 : Maps

Scales are used on maps in the same way that they are used in plans.
A scale of 1 : 50 000 is used on many Ordnance Survey maps.
This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km).

Converting measurements on a map
We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.

(a) Imagine we have measured a distance as 3 cm on this map, and we want to find out how far this is in real life.
To work out the distance in real life, we need to multiply this length by 50000.
This gives 3 cm × 50000 = 150000 cm which is 1500 m or 1.5 km.
Alternatively, we could have just remembered that each 1 cm on the map is 0.5 km in real life.
Hence, 3 cm on the map must be 3 × 0.5 km = 1.5 km in real life.

(b) Now imagine we want to walk 4.5 km in real life, and we need to find out how far this is on the map.
To work out the distance on the map, we need to divide this length by 50000.
4.5 km = 4500 m = 450000 cm. Dividing 450000 cm by 50000 gives a distance on the map of 9 cm.
Alternatively, we could have just remembered that each 0.5 km in real life is 1 cm on the map.
If we divide 4.5 km by 0.5 km we get 9, so the distance on the map must be 9 cm.

In general, it is easier to work out the answer to these type of questions by
working out what 1 cm on the map is equivalent to as a real life distance.

Example
A map has a scale of 1:25000.
This means that 1 cm on the map is 25000 cm in real life, which is 250 m or 0.25 km.
It is also useful to note that if 1 cm is 0.25 km, then 4 cm will represent 1 km in real life.

1 cm on the map represents 0.25 km in real life
4 cm on the map represents 1 km in real life

(a) The distance between two points on this map is 10 cm. What is the distance in real life?
Each 1 cm is worth 0.25 km, so the distance in real life is 10 × 0.25 km = 2.5 km.

(a) The distance between two points in real life is 7 km. What is the equivalent distance on this map?
Each 1 km is equivalent to 4 cm on the map, so the distance on the map will be 4cm × 7 = 28 cm.

Example Question

The map below shows three places, and is drawn to a scale of 1 : 300000.
Two distances on the map have been marked in centimetres.

Work out the answers to the questions on the right, then click Click on this button below to see the correct answer to see whether you are correct.

(a) What distance is 1 cm on the map equivalent to in real life (in km)?

(b) What is the distance in real life between Longton and Bowater (in km)?

The distance between Wyburn and Bowater is 19.5 km in real life.

(c) How far apart must Wyburn and Bowater be on the map (in cm)?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
A map has a scale of 1 : 50000.
What are the real life dstances (in km) represented by each of these lengths on the map?

(a) 4 cm km
(b) 10 cm km
(c) 3.2 cm km
(d) 5.1 cm km

Question 2
The distance between two places on a map is 6 cm. The map has a scale of 1 : 40000.

What is the actual distance between the two places (in km)?
km

Question 3
On a map with a scale of 1 : 3000000, the distance between Edinburgh and London is 18 cm.

What is the actual distance (in km) between these cities?
km

Question 4
Two towns are 15 km apart.

What would be the distance between the two towns on a map with a scale of 1 : 300000?
cm

Question 5
A tower is 2 km due north of a church. A windmill is 5 km east of the tower.

A map is to be drawn with a scale of 1 : 25 000.

(a) What will be the distance on the map between the church and the tower?
cm
(b) What will be the distance on the map between the tower and the windmill?
cm

Question 6
The distance between London and Birmingham is 165 km.

What would be the distance between these two cities on a map with a scale of:
(a) 1 : 500000 cm
(b) 1 : 1000000 cm
(c) 1 : 300000 cm
(d) 1 : 150000 cm

Question 7
On a map, a distance of 40 km, is represented by 32 cm.

What actual distance would be represented by 8 cm on the map?
km

Question 8
A map has a scale of 1 : 50 000.
A park is shown on the map as a rectangle measuring 6 cm by 4.2 cm.

What is the actual area of the park?
km˛


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Produced by A.J.Reynolds January 2001