Water is being pumped into an inverted right circular cone at while simultaneously…

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

Problem

Water is being pumped into an inverted right circular cone at

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

while simultaneously leaking out at

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

. The cone is

3\text{ m}

tall with a base radius of

2\text{ m}

. When the water depth is

1\text{ m}

, what is the rate of change of the radius of the water surface,

\dfrac{dr}{dt}

? (a)

-\dfrac{3}{2\pi}\,\text{m/min}

(b)

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

(c)

\dfrac{3}{2\pi}\,\text{m/min}

(d)

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