This question tests the application of derivatives in related rates, similar to Example 3 and Example 35 in the provided context. While those examples calculate the rate of change of area ($dA/dt$), this question requires calculating the rate of change of circumference ($dC/dt$). The key insight from the context is the application of the Chain Rule: $dy/dt = (dy/dx) \cdot (dx/dt)$. Since the circumference formula $C = 2\pi r$ is linear with respect to $r$, the rate of change is constant and does not depend on the specific radius value at a given instant, unlike the area calculation.