Q. 205.0( 1 Vote )

Answer :

Given: diameter of pipe = 20 cm

∴ radius of pipe = r_{p} = 20/2 = 10 cm = 0.1 m

Diameter of tank = 10 m

∴ radius of cylindrical tank = r_{c} = 10/2 = 5 m

Depth of cylindrical tank = height of cylindrical tank = h = 2 m

Rate of flow of water through pipe = 4 km/hr

1 km = 1000 m

4 km/hr = 4000 m/hr

Volume of water required to completely fill the tank is equal to the volume of cylinder

Time require to fill the tank = volume of cylindrical tank/volume of water flown through pipe per hr

volume of cylindrical tank = π × r_{c}^{2} × h

= 3.14 × 25 × 2

= 157 m^{3}

volume of water flown through pipe per hr = π × r_{p}^{2} × 4000

= 3.14 × 0.1^{2} × 4000

= 3.14 × 40

= 125.6 m^{3}/hr

Time require to fill the tank = 157/125.6

= 1.25 hrs

Therefore, it will take 1.25 hours to fill the tank completely.

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