Question

1: The scale of a map is given as 1:30000000. Two cities are 4 cm apart on
the map. Find the actual distance between them.​

Answer 1

Question:

The scale of a map is given as 1:30000000. Two cities are 4 cm apart on

the map. Find the actual distance between them.

Answer:

Let the map distance be x cm and actual distance be y cm, then

1 : 30000000 = x : y

$= > \frac{1}{3 \times {10}^{7} } = \frac{x}{y}$

Since x = 4 so,

$\frac{1}{3 \times {10}^{7} } = \frac{4}{y} \\ = > y = 4 \times 3 \times {10}^{7} = 12 \times {10}^{7} cm \\ = 1200km$

Thus, two cities, which are 4 cm apart on the map, are actually 1200 km away from each other.

Explanation:

• You Know that a map is a miniature representation of a very large region.
• A scale is usually given at the bottom of the map.
• The scale shows a relationship between actual length and the length represented on the map.
• The scale of the map is thus the ratio of the distance between two points on the map to the actual distance between two points on the large region.

• For Example: If 1 cm on the map represents 8 km of actual distance [i.e., the scale is 1cm:8km or 1:800, 000] then 2 cm on the same map will represent 16 km.
• Hence, we can Say that Scale of a map is based on the concept of Direct Proportion.