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?

Answers (1)

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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