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	{\noindent 21-120 Differential and Integral Calculus \hfill Summer Session I 2010\\}
	{\centering Quiz 4\medskip\\}
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		\begin{prob*}
		A circle is growing with a radius increasing at a rate of $3\unit{cm/s}$. Find a function (of the radius $r$) that gives the rate of change of the area of the circle.
		\end{prob*}
		\begin{soln*}
			The area of a circle is given by $A=\pi r^2$. Therefore, differentiating both sides with respect to $t$ we get \[ \frac{dA}{dt} = 2\pi r\cdot \frac{dr}{dt} \] We are given that $\frac{dr}{dt}=3\unit{cm/s}$. By substituting this in we get \[ \frac{dA}{dt} = 6\pi r \]
		\end{soln*}

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