Maximizing Volume of a 5-Sided Box w/ Cutout Corners

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SUMMARY

The discussion focuses on maximizing the volume of a five-sided box formed from a rectangular sheet of length L and width W, with x by x corners cut out. The key equations involved are the surface area (SA = 1LW + 2LH + 2WH) and volume (V = LWH). To achieve maximum volume, the optimal value of x must be determined, which can be approached through calculus or geometric reasoning. A tutorial link is provided for further guidance on similar problems.

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Dustinsfl
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Consider a sheet of length L and width W.

Each corner is cut out (x by x corners removed).

Detemine the value of x so when the corners are removed and flaps folded up, the five sided box formed will have maximum volume.

SA \(= 1LW + 2 LH + 2WH\) and V \(= LWH\).

I am not sure how to do this maximizing problem.
 
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See http://mathhelpboards.com/math-notes-49/folding-make-boxes-6366.html for a tutorial on this kind of problem. :D
 

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