Q10 of 79 Page 244

Water in a cylindrical tank of diameter 4 m and height 10 m is released through a cylindrical pipe of diameter 10 cm at the rate of 2.5 Km/hr. How much time will it take to empty the half of the tank? Assume that the tank is full of water to begin with.

Given,


Diameter of the cylindrical tank = 4 m


Radius of the cylindrical tank = 2 m


Height of the tank = 10 m


Diameter of the cylindrical pipe = 10 cm


Radius of the cylindrical pipe = = 5 cm


= 0.05 m


speed of water = 2.5 km/hr


= 2.5 x 1000 (1000 m = 1 km)


= 2500 m/hr


⇒ Volume of water discharged from the cylindrical pipe = Volume of cylindrical tank


⇒ Area of cross section time speed = r2 h


⇒ r2 time speed = r2 h


⇒ ()2 time 2500 = (2)2 (10)


⇒ () () time 2500 = (2) 2 (10)


⇒ Time = 2 10 () () ()


⇒ Time =


= 3.2 hour


= 3 hours 0.260 mins(1 hour = 60 minute)


= 3 hour 12 minute


Time taken to empty the half of the tank is 3 hour 12 minutes.


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