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.



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