Water is flowing into cylindrical tank of radius 7ft at the rate of 22 c.ft/sec. Then the rate of change in the water level is

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7/2 ft/sec

2/7 ft/sec

7 ft/sec

1/7 ft/sec

answer is B.

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Detailed Solution

$r = 7 \frac{dv}{dt} = 22 v = {πr}^{2} h \Rightarrow \frac{dv}{dt} = {πr}^{2} \frac{dh}{dt} \Rightarrow 22 = \frac{22}{7} \times 49 \times \frac{dh}{dt} \Rightarrow \frac{dh}{dt} = \frac{1}{7}$

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