Question

The radius of a cylindrical cistern is $10$ metres and its height is $15$ metres. Initially, the cistern is empty. We start filling the cistern with water through a pipe whose diameter is $50cm$. Water is coming out of the pipe at a velocity of $5m/s$. How many minutes will it take to fill the cistern with water?

• A. $80$ min
• B. $60$ min
• C. $75$ min
• D. $90$ min

Answer 1

The correct option is A $80$ min

Volume of a Cylinder $=\pi R^{2}h$$=\pi \times 10\times 10\times 15m^3$

Radius of pipe $=\frac{50}{2}cm=25cm=\frac{25}{100}m$

Since the pipe is cylindrical in shape, Volume $=\pi {\left(Radius\right)}^2\times height$

Here, height is considered as the distance traveled.

Hence, Volume of water coming out of pipe in one second $=\pi \times {\left(\frac{25}{100}\right)}^2\times 5m^3$

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

$=\frac{\pi \times 10\times 10\times 15}{\pi \times \frac{25}{100}\times \frac{25}{100}\times 5}$

$=4800seconds=\frac{4800}{60}=80$ minutes