Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3$ cm.

$6π\,cm^2/cm$

The correct answer is Option (1) → $6π\,cm^2/cm$

Let A be the area of a circle of radius $r$, then $A = πr^2$.

∴ The rate of change of area A with respect to its radius $r$

$=\frac{dA}{dr}=π.2r= 2πг$.

When $r = 3$ cm, $\frac{dA}{dr}=2π × 3 = 6π$.

Hence, the area of the circle is changing at the rate of $6π\,cm^2/cm$.