A right circular cone points downward and has a height of and a base radius of

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A right circular cone points downward and has a height of

5\text{ m}

and a base radius of

2\text{ m}

. Water drains through a hole at a constant rate of

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

. At the instant when the water depth is

4\text{ m}

, what is the rate of change of the water depth

\dfrac{dh}{dt}

? (The volume of a cone is

V=\tfrac{1}{3}\pi r^{2}h

.) (a)

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

(b)

\dfrac{75}{64\pi}\,\text{m/min}

(c)

-\dfrac{75}{64\pi}\,\text{m/min}

(d)

-\dfrac{45}{16\pi}\,\text{m/min}