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. - Mathematics

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

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

=7280×(1000m)^2×10/100m

=7280×10^5m^3

=7.28×10^8m3

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 × 10m3

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

= 3 × 2.412 × 108 m3

= 7.236 × 10m3

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

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APPEARS IN

NCERT Class 10 Maths
Chapter 13 Surface Areas and Volumes
Exercise 13.4 | Q 4 | Page 258