A farmer connects a pipe of internal diameter 12 cm from a Canal into a cylindrical tank in his field which is 10 m in diameter and 4 m deep.If water flows through the pipe at the rate of 5 km/h, in how much time will the tank be filled?
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The radius of the cylindrical tank, R = 12/2 = 6m = 600cm,
The depth of the tank, H = 2.5m = 250cm,
The radius of the cylindrical pipe, r = 25/2 = 12.5cm,
Speed of the flowing water, h = 3.6 km/hr = 360000m/3600s = 100cm/s
Now,
Volume of water flowing out from the pipe in a hour =
= 22/7 x 12.5 x 12.5 x 100
Also,
Volume of the tank =
= 22/7 x 600 x 600 x 250
So, the time taken to fill the tank = Volume of the tank / Volume of water flowing out from the pipe in a hour
= 5760 s = 5760/3600 = 1.6h
Also, the cost of water = 0.07 x 22/7 x 6 x 6 x 2.5 = Rs. 19.80
πr^2h = π R^2 H
r^2h = R^2 H
(6/100 ×6 /100) × (5× 5/18) ×t = (5×5)×4
t = (5×5×4×18 ×100×100)/(6×6×5×5)
t = 20000 seconds
= 20000/ 3600 hrs
= 50/9 hrs
= 5.556 hrs.