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Question

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of Rs 0.07 per m3.

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Solution

R = radius of cylinder = 6m

H = height of cylinder = 2.5m

r = radius of pipe = 252cm=18m

Rate of flow of water = 3.6kmhr

In 1 hr water upto a length of 3.6km = 3600m will come out of pipe.

let the tank be filled in 'x' hrs.

volume of water coming out of pipe in x hrs = volume of cylindrical tank.

(227×18×18×3600×(x)=227×6×6×2.5

18x18×3600×x = 6 x 6 x 2.5

3600×(x)=36x2.5x8x8

100×=8x8x2.5

1000×(x)=8x8x25

x=1610=1.6hrs

→x=1hr.36min.

Now,

costofwater=volumeofcylindricaltank×0.07

=22/7x6x6x2.5x0.07

= Rs.19.80.

The tank will be filled in 1hr.36 min and the cost of water will be Rs.19.80

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