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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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