The area $A$ of a circle with radius $r$ is given by the formula $A = \pi r^2$. To find the rate of change of the area with respect to its radius, we differentiate $A$ with respect to $r$.

Therefore, $\frac{dA}{dr} = \frac{d}{dr}(\pi r^2) = 2\pi r$.

(a) When $r = 3$ cm, we substitute this value into the derivative: $\frac{dA}{dr} = 2\pi (3) = 6\pi$. Thus, the rate of change of the area is $6\pi$.

(b) When $r = 4$ cm, we substitute this value into the derivative: $\frac{dA}{dr} = 2\pi (4) = 8\pi$. Thus, the rate of change of the area is $8\pi$.