This is a classic calculus optimization problem: cutting equal squares of side x from the four corners of a larger square sheet and folding up the edges to form an open-top box. The volume as a function of x is maximized by differentiating the volume formula and solving for the critical point that gives a genuine (non-degenerate) maximum.
If squares of side x are cut from each corner of a 12 cm square sheet, folding up the flaps creates a box with base...
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