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 km then show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75m wide and 3 m deep.

Answer 1

$\boxed{ \bf \: Correct \: Question : - }$

In one frontnight of a given month there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², then 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.

$\boxed{ \bf \: Solution : - }$

$\rm \: Given, \: area \: of \: the \: valley \: = \: 7280 \: km {}^{3}$

$\rm \: and \: height \: of \: rainfall \: in \: the \: valley$

$\: \: \: \: \: \: \: \: \: \: \: \: \rm = \: 10 \: cm \: = \: \frac{10}{100 \times 1000} \: km$

$\: \: \: \: \: \: \: \: \: \: \: \: \rm \bigg[ \because \: 1 \: cm \: = \: \frac{1}{100} \: m \: and \: 1 \: m \: = \: \frac{1}{1000} \: km \bigg]$

$\therefore \: \rm \: Amount \: of \: rainfall \: = \: Area \: of \: valley \times Height \: of \: rainfall$

$\rm \: \: \: \: \: \: \: \: \: \: \: \: \frac{7280 \times 10}{100 \times 1000} \: = \: 0.728 \: km {}^{3} \: \: \: \: \: \: \: \: \: \: ...(i)$

$\rm \: Also, \: given \: length \: of \: the \: river \: = \: 1072 \: km$

$\rm \: Breadth \: of \: the \: river \: = \: 75 \: m \: = \: \frac{75}{1000} \: km$

$\rm \: and \: height \: (depth) \: of \: the \: river \: = \: 3 \: m \: = \: \frac{3}{1000} \: km$

$\therefore \: \rm \: Volume \: of \: one \: cuboidal \: river \: = \: \red{l \times b \times h}$

$\rm \: \: \: \: \: \: \: \: \: \: \: \: = \: 1072 \times \frac{75}{1000} \times \frac{3}{1000} = 0.2412 \: km {}^{3}$

$\rm \: So, \: amount \: of \: the \: water \: in \: three \: rivers$

$\: \: \: \: \: \: \: \: \: \: \: \: \rm = \: 3 \times 0.2412 \: = \: 0.7236 \: km {}^{3} \: \: \: \: \: ...(ii)$

$\rm \: From \: Eqs. \: (i) \: and \: (ii) ,\: it \: is \: clear \: that \: total \: rainfall \: \\ \rm \: is \: approximately \: equivalent \: to \: the \: addition \: to \: the \: \\ \rm normal \: water \: of \: three \: rivers.$

$\boxed{\bf \purple{ Hope \: it's \: helps \: you : )}}$