# Calculus/Rate of Change

A circular oil slick spreads in such a way that its radius is increasing at a rate of 10 m/h. How fast is the area of the slick changing when the radius is 40 m? (In decimals)

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The trick for all such problems is to first write down a formula that relates the two given variables, in this case the radius and the area of a circle. We have $A = \pi r^2$. If we differentiate this with respect to time (bearing in mind the chain rule), we get $\displaystyle \frac{dA}{dt} = 2 \pi r \left( \frac{dr}{dt} \right)$.