The volume of a solid cylindrical rod is

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

Problem

V = \pi r^{2}L

, where the radius

r

and the length

L

vary with time. At one moment,

r = 0.50\text{ cm}

L = 20\text{ cm}

\dfrac{dr}{dt} = 0.010\text{ cm/min}

, and

\dfrac{dV}{dt} = 0.80\text{ cm}^{3}\!\big/\!\text{min}

. What is

\dfrac{dL}{dt}

at this instant? (a)

\displaystyle\frac{0.8}{\pi}-0.2\text{ cm/min}

(b)

\displaystyle\frac{3.2}{\pi}-0.8\text{ cm/min}

(c)

\displaystyle0.8\pi-3.2\text{ cm/min}

(d)

\displaystyle\frac{3.2}{\pi}+0.8\text{ cm/min}