If the rate of change of area of a circle is equal to the rate of cha…

The correct answer is option (2) → $\frac{1}{\pi}$ unit

from given question

$\frac{d(Area)}{dt}=\frac{d(diameter)}{dt}$

$\frac{d(πr^2)}{dt}=\frac{d(2r)}{dt}⇒2πr\frac{dr}{dt}=2\frac{dr}{dt}$

$⇒π=\frac{1}{r}$