Question

Water is flowing at the rate of $3km/h$ through a circular pipe of $20cm$ internal diameter into a circular cistern of diameter $10m$ and depth $2m$. In how much time, will the cistern be filled?

Answer 1

Step 1: Find the volume of the circular pipe

Given that,

The diameter of a circular pipe $=20cm$

Thus, the radius $r$ of a circular pipe $=\frac{20}{2}cm$ $(Radius=\frac{Diameter}{2})$

$=10cm$

$=\frac{1}{10}m$ $(1m=100cm)$

Water is flowing at the rate $=3km/h$

Let us consider the cistern will be filled in $xhours$

The height of a circular pipe $=3000xm$

We know that the volume of a cylinder is given by $V={\mathrm{\pi r}}^2\mathrm{h}$, where $r$ is radius and $h$ is height of the cone.

The volume of a circular pipe $V=\frac{22}{7}\times \frac{1}{10}\times \frac{1}{10}\times 3000x$ $(\mathrm{\pi }=\frac{22}{7})$

$=\frac{660x}{7}$

Step 2: Find the volume of the circular cistern.

Given that, the height of the circular cistern $=2m$,

And, the diameter of the circular cistern $=10m$

Thus, the radius of the circular cistern $=\frac{10}{2}$ $(Radius=\frac{Diameter}{2})$

$=5m$

The volume of a circular cistern $=\frac{22}{7}\times 5\times 5\times 2$

$=\frac{1100}{7}{m}^3$

Step 3: Find in how much time will the cistern be filled.

We have, Volume of circular pipe $=$ volume of a circular cistern

$\therefore \frac{660x}{7}=\frac{1100}{7}$

$\Rightarrow 660x=1100$

$\Rightarrow x=\frac{1100}{660}$

$\Rightarrow x=\frac{10}{6}$

$\Rightarrow x=1hour40minutes$

Hence, the cistern can be filled in $1hour40minutes$.