Which of the following gives the instantaneous rate of change of the area of a circle…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

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}

(b)

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

(c)

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

(d)

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