Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 53

Suppose that a stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60cm/s.

(a) We need to express the radius r of this circle as a function of the time t (in seconds).


$
\begin{equation}
\begin{aligned}
r(t) = 60t
\end{aligned}
\end{equation}
$


(b) Find A o r and explain, if A is the area of this circle as a function of the radius.



$
\begin{equation}
\begin{aligned}


A =& \pi r^2; \text{ but } r=60t\\
A =& \pi(60t)^2\\
A =& 3600 \pi t^2; \text{ the area of the circle as a function of time }
\end{aligned}
\end{equation}
$