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 m per second. In how much time will the tank be filled?

Answer 1

Radius of the water tank, R = $\frac{1.4}{2}$ = 0.7 m

Height of the water tank, H = 2.1 m

∴ Capacity of the water tank = $\mathrm{\pi }{R}^{2}H=\mathrm{\pi }{\left(0.7\right)}^2\times 2.1$ m³

Speed of the water flow = 2 m/s

Radius of the pipe, r = $\frac{3.5}{2}$ = 1.75 cm = 0.0175 m

Area of the cross section of the pipe = $\mathrm{\pi }{r}^2=\mathrm{\pi }{\left(0.0175\right)}^2$ m²

Volume of the water flowing out of the pipe in one second = Area of the cross section of the pipe × 2 m = $\mathrm{\pi }{\left(0.0175\right)}^2\times 2$ m³

Let the time taken to fill the tank be t seconds.

∴ Volume of the water flowing out of the pipe in t seconds

= Volume of the water flowing out of the pipe in one second × t

= $\mathrm{\pi }{\left(0.0175\right)}^2\times 2\times t$ m³

Now,

Volume of the water flowing out of the pipe in t seconds = Capacity of the water tank

$$\begin{gathered} \therefore \mathrm{\pi }{\left(0.0175\right)}^2\times 2\times t=\mathrm{\pi }{\left(0.7\right)}^2\times 2.1 \\ \Rightarrow t=\frac{{\left(0.7\right)}^2\times 2.1}{{\left(0.0175\right)}^2\times 2} \\ \Rightarrow t=1680\mathrm{s} \end{gathered}$$
$\Rightarrow t=\frac{1680}{60}$

⇒ t = 28 minutes

Thus, the tank will be filled in 28 minutes.