unit 2 sec 1.2

A map scale indicate how to determine distance on the ground from distance on a map. This line indicates that a distance of 2cm on the map represents 20km on the ground. By measuring a distance on the map in cm and using the map scale, you can obtain the corresponding distance on the ground.

Distance on the map can be measured by hand by laying a piece of string approximately along a route and then measuring the string, or by using an opisometor, an instrument with a small wheel for measuring distance on maps.

1cm represents 10km, this means this means that to find the ground distance in km, you multiply the map distance in cm by 10.

Map scales can be written in other forms, so you need to be familiar with these alternatives too. Often the scale of a map is given as say, 1:500000, or 1/500000 which is read as one to five hundred thousand. This means that any distance measured on the map represents 500000 time the distance on the ground. The number 500000 is called the scale factor of the map.

Example 1 converting map scales.

(A)       A map scale is given in words as 1cm represents 20km. What is the scale factor?

(B)      A map scale is given as 1:250000. Express the map scale in the form 1cm represents??km

Solution

(A)       Here, 1cm on the map represents 20km on the ground.

Convert 20km to cm by using 1km=1000m and 1m=100cm

Now ,

20km = (20×1000) m

=20000m

= (20000×100) cm

= 2000000cm

So 1 cm on the map represents 2000000cm on the ground. That is the map scale is 1: 2000000 so the scales factor is 2000000.

(B)      Here, 1cm on the map represents 250000cm on the ground

Convert 250000cm to km

  Now

250000cm = (250000÷100) m

=2500m

= (2500÷1000)km

= 2.5km

So the map scale is 1cm represents 2.5km

Example 2 using a map scale.

The scale of a map is 1:250000.

(A)       The distance on the map between two places is 7.5cm. What is the corresponding distance on the ground? Give you answer to two significant figures.

(B)      The distance on the ground between two places is 58.4km. what is the corresponding distance on the map? Give your answer to three significant figures.

Solution

(A)       A measurements of 1cm on the map represents 250000cm on the ground. So a map distance of 7.5cm represents a ground distance of (7.5×250000)cm now

(7.5×250000)cm = 1875000cm

= (1875000 ÷100 ÷1000) km

=18.75km

=19km (to 2 s.f)

Alternatively the map scale 1:250000 can be expressed as 1cm represents 2.5km, so a map distance of 7.5cm represents a ground distance of

(7.5×2.5)km = 18.75km = 19km (to 2 s.f)

(B) the scale factor is 250000, so the ground distance of 58.4km is represented by a map distance of (58.4÷250000)km now

(58.4÷250000)km = 0.0002336km

= (0.0002336×1000×100)cm

= 23.36cm

=23.4cm (to 3 s.f)

Alternatively the map scale 1:250000 can be expressed as 1cm represents 2.5 km, so a ground distance of58.4km is represented by a map distance of

(58.4÷2.5)cm =23.36cm =23.4cm (to 3 s.f)