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Question

Water is filled into a right inverted conical tank at a constant rate of 3m3/sec, whose semi vertical angle is cos145. The rate (in m/sec), at which the level of water is rising at the instant when the depth of water in the tank is 4m, is

A
1π
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B
12π
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C
13π
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D
14π
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Solution

The correct option is C 13π
As, θ=cos145,cosθ=45
From figure :

r=htanθ=3h4
V=πr2h3=3πh316dVdt=9πh216dhdt=3
At h=4:dhdt=13π

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