The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

$4\, cm^2/cm$

The correct answer is Option (2) → $4\, cm^2/cm$

$A=\pi r^2,\; C=2\pi r$

$\frac{dA}{dr}=2\pi r,\;\frac{dC}{dr}=2\pi$

$\frac{dA}{dC}=\frac{\frac{dA}{dr}}{\frac{dC}{dr}}=r$

At $r=4$

$\frac{dA}{dC}=4$

The required rate of change is $4\ \text{cm}$.