Question

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

• A. 218,000 minutes
• B. 14,080 minutes
• C. 140,800 minutes
• D. 21,660 minutes

Answer 1

The correct option is C 140,800 minutes

A water pipe is cylindrical in shape.

Rate of water flow = 6 mi/hr = 31,680 ft/hr

So, volume of water flowing through pipe in 1 hour is
$=\pi r^{2}h=\pi \times (10{)}^2\times 31,680$
$=(3.168\times {10}^6)\pi {\text{ft}}^3$

Volume of cylindrical tank is
$=\pi r^{2}h=\pi \times (15{)}^2\times 6$
$=\left(1350\right)\pi {\text{ft}}^3$


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

$\Rightarrow \frac{3.168\times {10}^6}{1350}=\frac{7040}{3}\text{hours}$
$=\frac{7040}{3}\times 60$
$=140,800\text{minutes}$