Question

The rate of change of area of a circle with respect to its radius at $r=2cm$ is

• A. $4$
• B. $2\pi$
• C. $2$
• D. $4\pi$

Answer 1

The correct option is D $4\pi$

Area $\left(A\right)$ of circle having radius $\left(r\right)$ id given by,

$A=\pi r^2$

Differentiate above w.r.t. $r$

$\frac{dA}{dr}=2\pi r$

Hence rate of change of area when radius $r=2$ cm is

$=\frac{dA}{dr}{|}_{r=2}=2\pi \left(2\right)2=4\pi$ cm