Water drains from a cylindrical tank of fixed radius at a constant rate of

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

Problem

Water drains from a cylindrical tank of fixed radius

2\text{ m}

at a constant rate of

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

. If

h(t)

is the water depth in meters, what is the instantaneous rate of change

\dfrac{dh}{dt}

(in m/min) when

h=3\text{ m}

? (a)

-\dfrac{1}{4\pi}

(b)

\dfrac{1}{8\pi}

(c)

-\dfrac{1}{8\pi}

(d)

-\dfrac{1}{32\pi}