Question

A hemispherical tank of radius $1\frac{3}{4}$ m is full of water. It is connected with a pipe which empties It at the rate of 7 liters per second. How much time will it take to empty the tank completely?

• A. 26.74
• B. 24.7
• C. 34.7
• D. 54.7

Answer 1

The correct option is A 26.74

Radius of the hemisphere $=\frac{7}{4}m=175cm$
$\therefore$ Volume of the hemisphere
$=\frac{2}{3}\times \pi \times 175\times 175\times 175c{m}^3$
The cylindrical pipe empties it at the rate of 7 litres ie, $7000c{m}^3$ of water per second.
Hence, the required time to empty the tank
$=(\frac{2}{3}\times \frac{22}{7}\times 175\times 175\times 175÷7000)sec$
$=\frac{2}{3}\times \frac{22}{7}\times \frac{175\times 175\times 175}{7000\times 60}min$
$=\frac{11\times 25\times 7}{3\times 2\times 12}min=\frac{1925}{725}min$
$=26.74min.nearly$.