Question

A cylindrical water tank of diameter $1.4m$ and height $2.1m$ is being fed by a pipe of diameter $3.5cm$ through which water flows at the rate of $2m/s$. Calculate the time, it takes to fill the tank.

Answer 1

given, water tank:

$diameter=1.4m⟹radius\left(r_1\right)=\frac{1.4}{2}=0.7m=70cm$ and

$height\left(h_1\right)=2.1m=210cm$

and pipe:

$diameter=3.5cm⟹radius\left(r_2\right)=\frac{3.5}{2}=\frac{7}{4}cm$ and

rate of flow = 2 m/s =200 cm/s

time taken by the pipe to fill the tank = $\frac{\text{volume of cylindrical water tank}}{\text{volume of the pipe}}$ $=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

(since, volume of cylinder = $\pi r^{2}h$)

on substituting,

$⟹\text{time taken}=\frac{\pi \times 70\times 70\times 210}{\pi \times \frac{7}{4}\times \frac{7}{4}\times 200}$

$=1680sec=\frac{1680}{60}min=28min$

therefore, time taken to fill the tank $=28$ minutes