Question

92. A pool has a uniform circular cross-section of radius 5 m and uniform depth 1-4 m. It is
filled by a pipe which delivers water at the rate of 20 litres per sec. Calculate, in minutes
the time taken to fill the pool. If the pool is emptied in 42 min. by another cylindrical
pipe through which water flows at 2 m per sec, calculate the radius of the pipe in cm.​

Answer 1

QUESTION:-

A pool has a uniform circular cross-section of radius 5 m and uniform depth 1-4 m. It is

filled by a pipe which delivers water at the rate of 20 litres per sec. Calculate, in minutes

the time taken to fill the pool. If the pool is emptied in 42 min. by another cylindrical

pipe through which water flows at 2 m per sec, calculate the radius of the pipe in cm.

ANSWER:-

Volume of pool =πR2h=π×5×5×1.4=35πm3=3500π litres

Volume of water coming out =50L per second

Time taken to fill the tank =5035000πsec

                                           =50×7×6035000×22 min

                                          =36.67 min

Let radius of pipe be ′r′ cm. Then

Volume of water coming out from pipe in 1 sec, =(πr2×200)cm3

Time required to empty =42min=42×60 sec

⇒πr2×20035×106cm3×π=42×60

⇒r2=42×60×20035×106=69.44cm

⇒r=69.44=8.33cm

__________^•^ ___________

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