The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
Answer & explanation
Correct answer: option 2
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 $4\ \text{cm}$.