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 $7litres$ per second. How much time will it take to empty the tank completely?

• A. $26.74min.$
• B. $26.54min.$
• C. $26.4min.$
• D. $26min.$

Answer 1

Answer: (A)

$26.74min.$

Suppose the pipe takes $x$ seconds to empty the tank.

Then,

The volume of the water that flows out of the tank in $x$ seconds =Volume of the hemispherical tank

The volume of the water that flows out of the tank $x$ in seconds= Volume of the hemispherical shell of radius $175cm$

$\Rightarrow 7000x=\frac{2}{3}\times \frac{22}{7}\times 175\times 175\times 175$

$\Rightarrow x=\frac{2}{3}\times \frac{22}{7}\times \frac{175\times 175\times 175}{7000}=1604.16seconds$

$\Rightarrow x=\frac{1604.16}{60}=26.74minutes$