Mathematics

Problem

Which of the following gives the instantaneous rate of change of the area

A

of a circle with respect to time

t

in terms of its radius

r

and the rate of change of radius

\dfrac{dr}{dt}

? a)

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

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

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

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