The area of a circular puddle is increasing at a rate of when its radius is

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

Problem

The area of a circular puddle is increasing at a rate of

12\text{ cm}^2\!/\text{s}

when its radius is

2\text{ cm}

. Determine the instantaneous rate of change of the radius at that moment. (a)

\dfrac{6}{\pi}\text{ cm/s}

(b)

\dfrac{3}{\pi}\text{ cm/s}

(c)

\dfrac{3}{2\pi}\text{ cm/s}

(d)

\dfrac{\pi}{3}\text{ cm/s}