A rectangle of perimeter \(24\text{ cm}\) is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
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Pay close attention to which side the rectangle is revolved around! Revolving around side \(y\) makes the volume proportional to \(x^2 y\), whereas revolving around side \(x\) would make the volume proportional to \(y^2 x\). This choice changes which variable is squared in the volume equation.
