Water is poured into a right circular cone whose base radius is and height is

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

Problem

Water is poured into a right circular cone whose base radius is

4\text{ m}

and height is

10\text{ m}

. The water always forms a similar cone as it rises. When the water depth is

5\text{ m}

, the volume of water is increasing at

3\text{ m}^3/\text{min}

. What is the rate at which the water depth is changing at that instant? (a)

\dfrac{9}{4\pi}\text{ m/min}

(b)

\dfrac{3}{4\pi}\text{ m/min}

(c)

\dfrac{1}{4\pi}\text{ m/min}

(d)

\dfrac{9}{16\pi}\text{ m/min}