# 9. 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?

Area of the cross-section of pipe is   $=\ \pi r^2$

$=\ \pi (0.1)^2\ =\ 0.01 \pi\ m^2$

Speed of water is given to be   =  3 km/hr

Thus, the volume of water flowing through a pipe in 1 min. is

$=\ \frac{3000}{60}\times 0.01 \pi$

$=\ 0.5 \pi\ m^3$

Now let us assume that tank will be completely filled after t minutes.

Then we write :

$t\times 0.5 \pi\ =\ \pi r^2h$

$t\times 0.5 \ =\ 5^2\times 2$

$t\ =\ 100$

Hence time required for filling of the tank completely is 100 minutes.

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