Mathematics

Mathematics

Problem

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan⁡−1(12)\tan^{-1}\left(\frac{1}{2}\right) . 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) 15π\frac{1}{5\pi} (B) 115π\frac{1}{15\pi} (C) 2π\frac{2}{\pi} (D) 110π\frac{1}{10\pi}

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