An inverted conical tank has a height of and a base radius of

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

Problem

An inverted conical tank has a height of

6\text{ m}

and a base radius of

3\text{ m}

. Because of sediment, the outflow rate (in cubic meters per minute) is modeled by

\dfrac{dV}{dt}=-0.5h

, where

h

is the current water depth in meters. When

h=4\text{ m}

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

\dfrac{dh}{dt}

? (a)

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

(b)

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

(c)

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

(d)

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