Question

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.

Answer 1

Area of the valley = 7280 km²

If there was a rainfall of 10 cm in the valley then amount of rainfall in the valley = Area of the valley × 10 cm

Amount of rainfall in the valley = 7280 km² × 10 cm
$$\begin{gathered} =7280\times {\left(1000\mathrm{m}\right)}^2\times \frac{10}{100}\mathrm{m} \\ =7280\times {10}^5{\mathrm{m}}^3 \\ =7.28\times {10}^8{\mathrm{m}}^3 \end{gathered}$$

Length of each river, l = 1072 km = 1072 × 1000 m = 1072000 m

Breadth of each river, b = 75 m

Depth of each river, h = 3 m

Volume of each river = l × b × h

= 1072000 × 75 × 3 m³

= 2.412 × 10⁸ m³

Volume of three such rivers = 3 × Volume of each river

= 3 × 2.412 × 10⁸ m³

= 7.236 × 10⁸ m³

Thus, the total rainfall is approximately same as the volume of the three rivers.