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 $2$ meter per second. In how much time the tank will be filled?

Answer 1

Step-1: Given data

Let the tank to be filled in x seconds .

Now we know that, we have to fill the tank.

Cylidrical tank dimensions:

Radius of tank $=\frac{1.4}{2}m$

Height of the tank$=2.1m$

Pipe dimesnions:

Radius of pipe$=\frac{3.5}{2}cm$

$=\frac{3.5}{2\times 100}m$

Therefore,

Step-2 :Volume of cylindrical tank

Volume of the cylindrical tank $={\mathrm{\pi r}}^2\mathrm{h}$

Volume of water that flows through the pipe in x seconds $=$ Volume of tank

By substituting the values, we get

$\begin{array}{rcl}\mathrm{\pi }{\left(\frac{3.5}{2\times 100}\right)}^{2}2\mathrm{x}& =& \mathrm{\pi }{\left(\frac{1.4}{2}\right)}^{2}2.1\\ \Rightarrow x& =& \frac{1.4^2\times 2.1\times {100}^2}{3.5^2\times 2}\end{array}$

On further calculations, we get

$$\begin{gathered} x=1680sec \\ x=\frac{1680}{60}min \\ x=28min \end{gathered}$$

Therefore, the tank will be filled in $28$ minutes.