Q. 105.0( 1 Vote )

# 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.

Answer :

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 = r^{2} h

⇒ r^{2} time speed = r^{2} 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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