Question

The water for a factory is stored in a hemispherical tank whose internal diameter is $14\text{m}$.The tank contains $50\text{kilolitres}$of water .Water is pumped into the tank to fill its capacity . Calculate the volume of the water pumped into the tank .

Answer 1

The internal diameter of hemispherical tank is $=14\text{m}$

So radius of tank $=\frac{\text{diameter}}{2}=\frac{14}{2}=7\text{m}$

Amount of water in the tank $=50\text{kl}$

We know that $1{\text{kl=1 m}}^3$

So amount of water in the tank $=50{\text{kl=50 m}}^3$

Volume of the hemispherical tank $=\frac{2}{3}{\mathrm{\pi r}}^3$$=\frac{2}{3}\times \frac{22}{7}\times 7\times 7\times 7=\frac{2156}{3}=718.66{\text{m}}^3$

Volume of the water pumped into the tank $=$volume of hemispherical tank $-$amount of water in the tank

$=718.66-50=668.66{\text{m}}^3$

Volume of the water pumped into the tank is $668.66{\text{m}}^3$