Question

A hemispherical tank, full of water, is emptied by a pipe at the rate of ${\displaystyle \frac{25}{7}}$litres per sec.

How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?

Answer 1

It is given that, diameter of base of tank = 3 m

${\displaystyle \therefore Redius,r=\frac{3}{2}m}$

Volume of water in the hemispherical tank

${\displaystyle =\frac{2}{3}\pi r^3}$

${\displaystyle =\frac{2}{3}\times \frac{22}{7}\times {\left(\frac{3}{2}m\right)}^3}$

${\displaystyle =\frac{99}{14}{m}^3}$

Rate of flow of water out of the pipe =${\displaystyle \frac{25}{7}}$litres / sec

Let the time taken to empty half the tank be t sec.

∴ Rate of flow of water × t sec ${\displaystyle =\frac{1}{2}\times }$Volume of water in the hemispherical tank

${\displaystyle \Rightarrow \frac{25}{7}\times t litre=\frac{1}{2}\times \frac{99}{14}{m}^3}$

${\displaystyle \Rightarrow \frac{25}{7}\times \frac{1}{1000}\times t{m}^3=\frac{1}{2}\times \frac{99}{14}{m}^3}$    ${\displaystyle (\therefore l litre=\frac{1}{1000}{m}^3)}$

${\displaystyle \therefore t=990}$

∴ Time taken to empty half the tank is (960 + 30) sec = 16 min 30 sec