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Question

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan1(12). Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is 10 m; is :

A
115π
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B
2π
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C
15π
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D
110π
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Solution

The correct option is C 15π

tanθ=12rh=12r=h2

Volume of the tank, V=13π(h2)2×h=112πh3
Differentiating both sides w.r.t. t, we get
dVdt=14πh2dhdt
dhdt=4πh2dVdt
dhdth=10=4π(10)2×5
dhdth=10=15π

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