Question

A rectangular tank is $80m$ long and $25m$ broad. Water flows into it through a pipe whose cross-section is $25{cm}^2$, at the rate of $16km$ per hour. How much the level of the water rises in the tank in $45$ minutes?

Answer 1

Let the level of water be risen by 'h' cm

Then,

Volume of water in the tank $=8000\times 2500\times h$

Area of cross-section of the pipe $=25c{m}^2$

Water coming out of the pipe forms a cuboid of base area $25c{m}^2$ and length equal to the distance traveled in 45 minutes with the speed of 16 kmph

Length $=16000\times 100\times \frac{45}{60}$

Volume of water coming out of pipe in 45 minutes $=25\times 16000\times 100\left(\frac{45}{60}\right)$

Now, Volume of water in the tank $=$ Volume of water coming out of the pipe in 45 minutes

$\Rightarrow 8000\times 2500\times h=16000\times 100\times \frac{45}{60}\times 25$

$\Rightarrow h=\frac{16000\times 100\times 45\times 25}{8000\times 2500\times 60}$

$\Rightarrow h=1.5cm$