CBSE Class 10 Answered

This question has a typographical error. In order to prove the required result, the area of valley should be

7236 km²

Solution:

Assume the rivers to be cuboidal,

Volume of water in river-1 = length x breadth x depth

                                               = 1072 x 10³ x 75 x 3 m³ = 2412 x 10⁵ m³

All three rivers have equal amount of water. Therefore,

Total volume of water in the river = 3 x (2412 x 10⁵) m³ =7236 x 10⁵m³ .....................(1)

Area of valley = 97820 km²= 97820 x 10⁶ m²

If the rain fall is of 10 cm, the volume of water in the valley due to rainfall = Area of the valley x rainfall

                                                              = 97820 x 10⁶ x 10 x 10^-2m³

                                                             = 97820 x 10⁵ m³                           .............................(2)

The volume of water for the two cases are different (from eqn (1) & (2)).

Therefore, prove accordingly.