At a particular instant

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

At a particular instant, the volume

V

of a growing sphere (in

\text{cm}^3

) depends on its radius

r

(in

\text{cm}

) and satisfies

\dfrac{dV}{dr}=4\pi r^2

. The radius is increasing at a rate of

\dfrac{dr}{dt}=2\,\text{cm/s}

. State the units of

\dfrac{dV}{dt}

at this instant and briefly explain how these units arise from the given rates.