The area of a circle of radius changes as the radius changes over time

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The area

A

of a circle of radius

r

changes as the radius changes over time. Which expression gives

\dfrac{dA}{dt}

in terms of

r

and

\dfrac{dr}{dt}

? (a)

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

(b)

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

(c)

\dfrac{1}{2}\pi r\dfrac{dr}{dt}

(d)

\pi r\dfrac{dr}{dt}