Lesson 1, Topic 3
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Map Scales

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Scale on a map is defined as the ratio of actual distance to distance on map.

Map scale = $$\frac {actual \; distance}{distance \; on \; map}$$

Map scales are normally written in the ratio form 1 : 7 e.g. 1 : 50 000 means 1cm represents 50 000cm.

Example 4

Rewrite the scales in ratio form

a. 1cm represents 10m
b. 1cm represents 20cm
c. 1cm represents 20km

Solution

a. 1cm represents 10m

both have different units: change 10m to cm.

1m =  100cm

10m = 10 x 100cm = 1000cm

Scale = 1 : 1000

b. 1cm represents 20cm

both are in the same units

scale = 1 : 20

c. 1cm represents 20km

convert 20km to cm

1km  = 1000m

= 1000 x 100cm

1km = 100 000cm

20km = 20 x 100 000cm

= 2 000 000cm

Scale = 1 : 2000 000

Example 5

Two cities are 70km apart. The distance between them is 20cm on the map. What is the scale of the map?

Solution

Let the scale be 1 : n

1 cm → n cm

20 cm → 70 km

20 x n cm = 70km x 1

Convert 70km to cm

1km = 100 000cm

70km = 7 000 000cm

:- 20 x n cm = 7 000 000 cm

20n = 7 000 000

n =   $$\frac {7\;000\; 000}{20}$$

n = 350 000

The scale = 1 : 350 000

OR

Using the formula

Map scale = $$\frac {actual \; distance}{distance \; on \; map} \\ = \frac {7\;000\;000}{20} \\ = \scriptsize 350\;000$$

The scale on map = 1 : 350 000

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