\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

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A wire with a total length of 12in can be bent into a circle, square, or cut to make both a circle and a square. How much of the wire should be used for the circle, if the total area enclosed for both shapes is to be minimized. What about if we wanted to maximize it?


Solution: