**Question:**

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?

**Solution:**

Radius of the cylindrical tank $=0.7 \mathrm{~m}$

Height of the cylindrical tank $=2.1 \mathrm{~m}$

Volume of the cylindrical tank $=\pi(0.7)^{2}(2.1) \mathrm{m}^{3}$

Length of the water column flown from the pipe in $1 \mathrm{~s}=2 \mathrm{~m}$

Let the time taken to completely fill the water tank be $x$ sec.

Length of the water column flown from the pipe in $x$ sec $=2 x \mathrm{~m}$

Radius of the pipe $=1.75 \mathrm{~cm}=0.0175 \mathrm{~m}$

Volume of the water column flown from the pipe in $x \sec =\pi(0.0175)^{2}(2 x) \mathrm{m}^{3}$

Volume of the cylindrical $\tan \mathrm{k}=$ Volume of the water column flown from the pipe

$\pi(0.7)^{2}(2.1)=\pi(0.0175)^{2}(2 x)$

$\mathrm{x}=\frac{0.7)^{2}(2.1)}{0.0175)^{2}(2)}=1680 \mathrm{sec}=28 \min$

Thus, the time required to fill the water tank is 28 min.