Maximizing Volume Formula for Given Box Dimensions and Cut Size

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To maximize the volume of a box defined by L = 1.414w, W = w, and a cut size x, the volume formula is V = x(1.414w - 2x)(w - 2x). The initial attempt yielded V = 4x^3 - 4.818x^2w + 1.414w^2, but this was not the correct general formula for maximum volume. The user later resolved the issue independently. The discussion highlights the importance of correctly applying the dimensions and cut size in volume calculations. Ultimately, the correct approach leads to the desired maximum volume formula.
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Homework Statement


A box is given with a L = 1.414w and W = w and a cut size = x. Find the general formula for the maximum volume.

Homework Equations


L = 1.414w - 2x
W = w - 2x
H = x

The Attempt at a Solution


V = x(1.414w - 2x)(w - 2x)
V = 4x3 - 4.818x2w + 1.414w2
Apparently this isn't the general formula for max volume, so someone please help.
 
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Never mind guys. I figured it out.
 
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