Question

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his 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?

 

Answer 1

The internal radius of the pipe is 10 cm=0.1 m. The water is flowing in the pipe at 3km/hr = 3000m/hr.

Let the cylindrical tank will be filled in t hours. Therefore, the length of the flowing water in t hours is = 3000 x t meter

Therefore, the volume of the flowing water is V₁= π x (0.1)² x 3000 x t m³

The radius of the cylindrical tank is 5 m and the height is 2 m. Therefore, the volume of the cylindrical tank is

V₂ =  π x (5)² x 2 m³

Since, we have considered that the tank will be filled in t hours; therefore the volume of

the flowing water in t hours is same as the volume of the cylindrical tank. Hence, we have

V₁ = V₂

⇒`pixx(5)^2=pixx(0.1)^2xx3000xxt`

⇒`t=((5)^2xx2)/((0.1)^2xx3000)`

⇒`t=3/5`hours

`t=(5xx60)/3=100` minutes

Hence, the tank will be filled in 1 hour 40 minutes