Question

Water is flowing at the rate of $3$ km/hr 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?

• A. $2$ hours
• B. $1$ hour $40$ min
• C. $1$ hour $15$ min
• D. $2$ hour $30$ min

Answer 1

The correct option is B $1$ hour $40$ min

The cistern is in cylindrical shape.
Volume of a cylinder $=\pi R^{2}h$
Radius of cistern $=\frac{10}{2}m=5m$
Hence, volume of the cistern $=\pi \times 5\times 5\times 2m^3$
Radius of pipe $=\frac{20}{2}cm=10cm=\frac{10}{100}m=\frac{1}{10}m$
Since the pipe is cylindrical in shape, Volume $=\pi {\left(Radius\right)}^2\times height$

Here, height is considered as the distance traveled $=3km=3000m$.
Hence, volume of water coming out of pipe in one hour $=\pi \times {\left(\frac{1}{10}\right)}^2\times 3000m^3$

Now, time taken to fill the cistern $=\frac{\text{Volume of the cistern}}{\text{Volume of water coming out of pipe in one hour}}$

$=\frac{\pi \times 5\times 5\times 2}{\pi \times \frac{1}{10}\times \frac{1}{10}\times 3000}=\frac{5}{3}$ hours

$=1$ hour $+\frac{2}{3}$ hours $=1$ hour $+\frac{2}{3}\times 60$ min $=1$ hour $40$ minutes