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Question 18
Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?


Solution

Given , radius of tank, r1=40 cm.
Let height of water level in tank in half an hour = h1
Also, given internal radius of cylindrical pipe r2=1 cm
And speed of water = 80 cm/s. i.e in 1sec water flow = 80 cm.
in 30 ( min) water flow =80×60×30=144000 cm
According to the question.
Volume of water in cylindrical tank = Volume of water flow from the circular pipe In half an hour
πr21h1=πr22h2
40×40×h1=1×1×144000h1=14400040×40=90 cm
Hence, the level of water in cylindrical tank rise 90 cm in half an hour.


Mathematics
NCERT Exemplar
Standard X

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