Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 5 feet?
15.71
\times
ft²/min
Recall that to find the rate at which the area of the circle changes with respect to the radius, it is necessary to find a relationship between the two quantities. Sketch the described situation and assign the variables $A$, $r$, and $t$ to the area of the circle, the radius, and time, respectively. What is the formula relating the area of a circle and its radius? How can this relation be used to find an expression for $\frac{dA}{dr}$ in terms $r$ and $\frac{dr}{dt}$?