Question

A pool has a uniform cross-section of radius $5$ m and uniform depth $1.4m$. It is filled by a pipe which delivers water at the rate of $20litrespersec$. Calculate, in minutes, the time taken to fill the pool. If the pool emptied in $42$ min. by another cylindrical pipe through which waters flows at $2$ m per sec, calculate the radius of the pipe of the pipe in cm.

Answer 1

Volume of the pool$=\pi r^{2}h$

$=\frac{22}{7}\times 5^2\times 1.4=110m^3$

$20litres=0.02m^{3}persecond$

Time taken to fill the pool$=\frac{110}{0.02}=5500sec$

$=\frac{5500}{60}=\frac{275}{3}minutes=91\frac{2}{3}minutes$

Let the radius of the outlet be $rm$

$42minutes=42\times 60=2520secs$

Time taken to fill the tank$=\frac{110}{2\times \pi r^2}$

$\Rightarrow 2520=\frac{110}{2\times \pi r^2}$

$\Rightarrow r^2=\frac{110}{2\times \frac{22}{7}\times 2520}=\frac{1}{144}$

$\therefore r=\frac{1}{12}m$

Radius of the pipe$=\frac{1}{12}\times 100=\frac{25}{3}cm$