Question

A hemispherical tank full of water is emptied by a pipe at the rate of $\frac{25}{7}$ litres per second. How much time will it take to half-empty the tank, if the tank is $3$ metres in diameter?

Answer 1

Given,

The diameter of hemispherical tank $D=3m$

Hence, the radius of hemispherical tank $R=\frac{D}{2}=1.5m$

The total volume of water in the hemispherical tank $V=\frac{2}{3}\pi R^3$

$V=\frac{2}{3}\times \frac{22}{7}\times (1.5{)}^3{m}^3$

$V=\frac{44}{21}\times 3.375m^3$

$V=\frac{148.5}{21}{m}^3$

$V=\frac{148500}{21}liters$ $(\because 1m^3=1000liter)$

Hence, the total volume of water in the hemispherical tank is $\frac{148500}{21}liters$

Volume of half-empty tank $=\frac{V}{2}=\frac{74250}{21}liters$

Given that time required to empty the tank by $\frac{25}{7}liters$ of water $=1second$

Hence, the time required to empty the tank by $1liter$ of water $=\frac{7}{25}second$

Now, time taken to half-empty the tank $\frac{74250}{21}liters$ of water $=\frac{7}{25}\times \frac{74250}{21}seconds$

$=990seconds$

.

$=16.5minutes$ $(\because 1minute=60seconds)$

Hence, time taken to half-empty the tank is $16.5minutes$