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# Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.

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In the given problem shape of the pipe is cylindrical and tank shape also cylindrical. This question was asked in 2013 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 811, exercise 17B, problem number 24

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1. Given data,

radius of cylindrical pipe , r = 1cm

radius of cylindrical tank , R = 40cm

water is flowing through a cylindrical pipe into cylindrical tank at the rate of 40cm/s.

length of water through pipe , l= rate × time taken

= 40cm/s × 1/2 hr

= 40cm/s × 30 × 60

= 40 × 1800 cm

= 72000 cm

volume of water flows through pipe = volume of water rise in cylindrical tank

πr² × l = πR² × h

(1)² × 72000  = (40)² × h

72000 = 1600  × h

h = 720/16

h = 45 cm

∴ 45 cm rise in the level of water in the rank in half an hour

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