Question
Fri March 06, 2015 By: Rahul

A pool has a uniform circular cross-section of radius 5m and uniform depth 1.4m. It is filled by a pipe which delivers water at a rate of 20 litres per sec. Calculate,in minutes, the time taken to fill the pool. If the pool is emptied in 42min. by another cylindrical pipe through which water flows at 2m per sec, calculate the radius of the pipe in cm.

Expert Reply
Prasenjit Paul
Fri March 06, 2015
V o l u m e space o f space t h e space p o o l equals πr squared straight h equals 22 over 7 cross times 5 squared cross times 1.4 equals 110 space straight m cubed 20 space litres equals 0.02 space straight m cubed divided by sec Time space taken space to space fill space the space pool equals fraction numerator 110 over denominator 0.02 end fraction equals 5500 space sec equals 5500 over 60 equals 275 over 3 minutes equals 91 2 over 3 minutes Let space the space radius space of space the space outlet space pipe space be space straight r space straight m 42 space minutes equals 42 cross times 60 equals 2520 space sec Time space taken space to space fill space the space tank equals fraction numerator 110 over denominator 2 cross times πr squared end fraction rightwards double arrow 2520 equals fraction numerator 110 over denominator 2 cross times πr squared end fraction rightwards double arrow straight r squared equals fraction numerator 110 cross times 7 over denominator 2520 cross times 2 cross times 22 end fraction rightwards double arrow straight r squared equals 1 over 144 therefore straight r equals 1 over 12 straight m Radius space of space the space pipe equals 1 over 12 cross times 100 equals 25 over 3 cm
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