Question

In the extract of Survey of India map G43S7, prepared on a scale of 2 cm to 1 km, a child finds the length of the cart track between two settlements is 7.6 cm. Find:

1. the actual length of the cart track on the ground. 
2. actual area of a grid square, if each has an area of 4 cm².

Answer 1

Given:

Scale of map: 2 cm represents 1 km.

Map length of cart track = 7.6 cm.

Area of each grid square on map = 4 cm².

Step-wise calculation:

a. Actual length of the cart track:

2 cm → 1 km

⇒ 1 cm → `1/2` km = 0.5 km

Map length 7.6 cm → Ground length

= 7.6 × 0.5 km

= 3.8 km

In metres:

3.8 km = 3.8 × 1000 

= 3800 m

b. Actual area of a grid square:

1 cm on map = 0.5 km

⇒ 1 cm² on map = (0.5 km)² = 0.25 km²

Therefore, 4 cm² on map

= 4 × 0.25 km²

= 1.0 km²

In square metres: 

1.0 km² = 1,000,000 m²