An inverted conical tank has height and radius at the top

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

An inverted conical tank has height

9\text{ m}

and radius

3\text{ m}

at the top. Water is pumped in at

2.0\text{ m}^{3}\!\big/\!\text{min}

, but simultaneously leaks out at

0.5\text{ m}^{3}\!\big/\!\text{min}

. When the water depth is

6\text{ m}

, what is the rate at which the depth is changing? (a)

\dfrac{1}{8\pi}\text{ m/min}

(b)

\dfrac{3}{8\pi}\text{ m/min}

(c)

\dfrac{1}{2\pi}\text{ m/min}

(d)

\dfrac{5}{8\pi}\text{ m/min}