# In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

**Solution:**

Since there was a rainfall of 10 cm in a river valley of area 7280 km² the volume of the rainfall will be calculated by

Volume of the rainfall = Area of the river valley x height of rainfall in the river valley Since the dimensions of three rivers are known, we can calculate the volume by

Volume of the river = length x breadth x height

Area of the Valley, A = 7280 km² = 7280 × 1000000 m² = 7.28 × 10^{9} m²

Height of rainfall in a fortnight, h = 10 cm = 10/100 m = 0.1 m

Volume of the rainfall = Area of the river valley × height of rainfall in the river valley

= 7.28 × 10^{9} m² × 0.1 m

= 7.28 × 10^{8} m³

Length of river, l = 1072 km = 1072 × 1000 m = 1.072 × 10^{6} m

Width of river, b = 75 m

Depth of river, h = 3 m

Volume of 3 rivers = 3 × volume of 1 river

= 3 lbh

= 3 × 1.072 × 106 m × 75 m × 3 m

= 723.6 x 10^{6} m³

= 7.236 × 10^{8} m³

Since 7.236 × 10^{8} m³ is approximately equivalent to 7.28 × 10^{8} m³

Therefore, we can say that total rainfall in the valley was approximately equivalent to the addition of normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

**Video Solution:**

## In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.5 Question 4 :

In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Its proven that the total rainfall in the valley was approximately equivalent to the addition of normal water of three rivers each 1072 km long, 75 m wide and 3 m deep since the area of the valley and the volume of the the rivers is approximately the same.