A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his Held, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

AcademicMathematicsNCERTClass 10

Given:

The internal diameter of the pipe$=20\ cm$.

Diameter of cylindrical tank$=10\ m$.

Depth of the tank$=2\ m$ and rate of water flow in the pipe$=3\ km/h$.

To do:

We have to find the time taken to fill 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 $= v=3\ km/h=3\times 1000=3000\ m/h$

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 cylindrical tank

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

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

$\Rightarrow t=\frac{5^{2} \times 2}{\left(\frac{1}{10}\right)^{2} \times 3000}$

$\Rightarrow t=\frac{50}{30}$

$\Rightarrow t=1\frac{2}{3}$

$\Rightarrow t=\ 1\ hour\ 40\ minutes$

Therefore, it will take 1 hour and 45 minutes to fill the tank completely.

raja
Updated on 10-Oct-2022 13:25:34

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