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प्रश्न
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?
उत्तर
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
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