A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field,

Question:

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, 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?

Solution:

Water speed $=3 \mathrm{~km} / \mathrm{hr}=\frac{\mathbf{3 0 0 0}}{\mathbf{6 0}} \mathbf{m} / \mathbf{m i n}$

$=50 \mathrm{~m} / \mathrm{min}$

Diameter of the pipe = 20 cm

i.e., radius $=10 \mathrm{~cm}=\frac{\mathbf{1}}{\mathbf{1 0}} \mathbf{m}$

Water tank has 2m depth and 10 m diameter, i.e., radius 5 m

Let the required time to fill the tank be n minutes.

Then water flowing through the pipe in n minutes = Volume of the water tank.

$\Rightarrow \pi \times\left(\frac{\mathbf{1}}{\mathbf{1 0}}\right)^{2} \times\{\mathrm{n} \times 50\}=\pi \times(5)^{2} \times 2$

$\frac{\mathbf{1}}{\mathbf{1 0 0}} \times n \times 50=50 \Rightarrow n=100$

Hence, the required time is 100 minutes.

 

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