Question

16. A map has a scale of 1 cm to 500 m.

(i) Express the scale of the map in the form 1 : n,
where n is an integer.
(ii) If the distance between two districts is 28 km,
find the corresponding distance on the map.
(iii) If a jungle has an area of 12 cm² on the map,
calculate its actual area in square kilometres.

Answer 1

(i) 1 : 50,000

(ii) 56 cm

(iii) 3 km²

Explanation:

You want various measures related to a map with a scale of 1 cm : 500 m.

(i) Scale

The ratio of 1 cm to 500 m can be written as ...

0.01 m : 500 m = 1 : 50,000 . . . . . . . multiply both sides by 100/m

The scale of the map is 1 : 50,000.

(ii) 28 km

A ground distance of 28 km will be a map distance of ...

(28 km)/(50,000) = 0.56 m = 56 cm

The corresponding map distance is 56 cm.

(iii) Area

The given ratio can be squared to find the actual area:

1 cm : 0.5 km ⇒ (1 cm)² : (0.5 km)² = 1 cm² : 0.25 km²

Multiplying by 12 gives ...

12 cm² : (0.25·12) km² = 3 km²

The actual area is 3 square kilometers.

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