# A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep? if the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?

Given: Internal diameter of the pipe$=20\ cm$, diameter of cylinderical tank$=10\ m$, depth of the tank =2 m and rate of water-flow in the pipe$=4\ km/h$

To do: To find the time taken to be filled the tank completely.

Solution: For the given tank.

Diameter $=10\ m$

Radius, $R = \frac{Diameter}{2}=5\ m$

Depth, $H= 2\ m$

For the pipe ,

Internal diameter$=20\ cm$

Internal radius of the pipe , r =$\frac{20}{2} =10\ cm =\frac{10}{100}\ m=\frac{1}{10} m$

Rate of flow of water $= v=4\ km/h=4\times 1000=4000\ m/h$

Let us assume t be the time taken to fill the tank,

So, the water flown through the pipe in t hours will equal to the volume of the of the cylinderical tank

$\therefore \pi r^{2} \times v\times t=\pi \times R^{2} \times H$

$\Rightarrow t=\frac{R^{2} H}{r^{2} \times v}$

$\Rightarrow t=\frac{5^{2} \times 2}{\left(\frac{1}{10}\right)^{2} \times 4000}$

$\Rightarrow t=\frac{50}{40}$

$\Rightarrow t=1\frac{1}{4}$

$\Rightarrow t=\ 1\ hour\ 15\ minues$

Therefore, it will take 1 hour 15 minutes to fill the tank completely.

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Updated on: 10-Oct-2022

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