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?

Given

Internal radius of the pipe = 10 cm = 0.1m

Water flowing in the pipe at 3km/hr = 3000m/hr

Let the cylindrical tank will be filled in t hours

Hence, the length of the flowing water in t hours = 3000 x t meter

Hence, 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. Thus 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, hence the volume of the flowing water in t hours is equal to the volume of the cylindrical tank. Thus, we have

V1 = V2

π x (0.1)2 x 3000 x t = π x (5)2 x 2

t = (5)2 x 2/(0.1)2 x 3000

t = (5 x 5 x 2)/30

t = 5/3 hours

t = 5/3 x 60 min

We get,

t = 100 minutes

t = 1 hour 40 minutes

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

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