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# 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, then in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of 0.07 per m³

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This question was asked in 2009 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 811, exercise 17B, problem number 27

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given data

the radius of the cylindrical tank, R = 12/2 = 6 m = 600 cm,

the depth of the tank, H = 2. 5 m = 250 cm,

the radius of the cylindrical pipe, r = 25/2 = 12. 5 cm

speed of the flowing water =  3.6km/hr

In 1 hr water up to 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.

πr²h = πR²H

(22/7) (1/8)² (3600) (x) = (22/7) (6)² (2.5)

(1/8)² (3600) (x) = (6)² (2.5)

x = [ (6)² (2.5) ] / [ (1/8)² (3600) ]

3600(x) = 36 *2.5 * 8

x = 16/10

x = 1.6 hrs

x = 1 hr.36 min.

Now,

cost of water = volume of cylindrical tank * 0.07

= πr²h * 0.07

= [22/7] * 6² * 2.5 * 0.07

= 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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