The area of a circle of radius is given by

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

Problem

The area

A

of a circle of radius

r

is given by

A=\pi r^{2}

. Which of the following expresses the instantaneous rate of change of the area with respect to time? (a)

2\pi r^{2}\,\dfrac{dr}{dt}

(b)

\pi r\,\dfrac{dr}{dt}

(c)

2\pi r\,\dfrac{dr}{dt}

(d)

\pi\left(\dfrac{dr}{dt}\right)^{2}