Question

A water pipe of internal diameter 20 cm from a canal is connected to a cylindrical tank of radius 5 m and height 2 m. If water flows through the pipe at 6 km/hr, how much time will it take for the tank to be filled?

• A. 60 minutes
• B. 50 minutes
• C. 40 minutes
• D. 30 minutes

Answer 1

The correct option is B 50 minutes

A water pipe is cylindrical in shape.

Rate of water flow = 6 km/hr = 6,00,000 cm/hr

So, volume of water flowing through pipe in 1 hour is
$=\pi r^{2}h=\pi \times (10{)}^2\times 6,00,000$
$=(6\times {10}^7)\pi {\text{cm}}^3$

Volume of cylindrical tank is
$=\pi r^{2}h=\pi \times (500{)}^2\times 200$
$=(5\times {10}^7)\pi {\text{cm}}^3$


Let t be the time taken to fill the cylindrical tank = $\frac{Volumeofcylindricaltank}{Volumeofwaterflowingthroughthepipein1hr}$

$\Rightarrow \frac{5\times {10}^7}{6\times {10}^7}=\frac{5}{6}\text{hours}$
$=\frac{5}{6}\times 60$
$=50\text{minutes}$