Question

The radius of a cylinder of a circular oil slick expands at a rate of 2m/min. How fast is the area of the oil slick increasing when the radius is 25m?

Answer 1

\[
A(t)=\pi [r(t)]^2
\]They're both functions of \(t\). You an differentiate with chain rule: \[
A'(t)=\pi 2r(t)r'(t)
\]

Answer 2

You can plug in the values they gave you.
\(r=25\) and \(r'=2\): \[
A'(t) = 2\pi(25)(2)
\]