The radius of a circle is decreasing at a constant rate of \(0.2\) centimeters per second. In terms of the circumference \(C\), what is the rate of the change of the area of the circle, in square centimeters per second?

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We are given the following quantities:

$$ \frac{dr}{dt}=-0.1 $$

We are asked to find \(\dfrac{dA}{dt}\), which we can derive using the area formula.

$$ A=\pi r^2 $$ $$ \frac{dA}{dt}=2\pi r \frac{dr}{dt} $$

Note that circumference is equal to \(2\pi r\), so we can make the following substitution:

$$ A = C \frac{dr}{dt} $$ $$ A = \boxed{-(0.1)C} $$