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

Answers (1)

Answer : 668.66 \; m^{3}

We know that Volume of hemispherical tank=\frac{2}{3}\pi r^{3}

Where, r = radius of hemispherical tank

Now, internal diameter of hemispherical tank is given as 14 m

So, internal radius of hemispherical tank=\frac{14}{2}=7\; m

Tank contains 50 kL of water

We have, 1000 \; L=1\; m^{3}

So, 1\; kL=1\; m^{3}

This means that tank contains 50\; m^{3} of water

\Rightarrow Volume of hemispherical tank =\frac{2}{3}\times\frac{22}{7}\times \left ( 7 \right )^{3}=\frac{2156}{3}=718.66\; m^{3}

Now, as we are given that the already tank contains 50 kilolitres of water

Volume of water pumped into the tank = Total Volume of hemispherical tank -50\; m^{3}

Volume of water pumped into the tank =\left ( 718.66-50 \right )m^{3}=668.66\; m^{3}

Hence the answer is 668.66\; m^{3}

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