Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If, water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?

• A. 80
• B. 100
• C. 150
• D. 200

Answer 1

The correct option is B

100

Given that diameter of pipe, d = 20 cm
Then, radius of pipe,
$r=\frac{20}{2}=10cm=0.1m$
Speed of water flowing through pipe = 3 $km/h$ = 3000 $m/h$

Pipe is in the form of a cylinder.
So, volume of water flowing through pipe in 1 hour
$=\pi r^{2}h=\pi \times 0.1\times 0.1\times 3000=30\pi m^3$

Let the cylindrical tank be filled in $x$ hours.

Then, volume of water flowing through pipe in $x$ hours
$=30x\pi m^3$

Also it is given that,
diameter of cylindrical tank, $d_1=10m$
$\Rightarrow$ radius of cylindrical tank, $r_1=\frac{10}{2}=5m$
Height of cylindrical tank, $h_1=2m$

Volume of cylindrical tank
$=\pi (r_1{)}^2{h}_1=\pi \times 5\times 5\times 2=50\pi m^3$

Now, volume of water flowing through pipe in $x$ hours = volume of cylindrical tank

$\Rightarrow 30x\pi =50\pi$

$\Rightarrow x=\frac{50}{30}=\frac{5}{3}hours$

$i.e.,x=\frac{5\times 60}{3}minutes=100minutes$

$\therefore$ The tank will be filled in 100 minutes.