well, the cutouts on each corner have dimensions x times x, or area x^2
So the box has dimensions. So the dimensions of the box will be LxWxH (length, width, height).
30=L+2x (x is the height)
30=W+2xfrom the metal dimensions.
so L=30-2x
W=30-2x
Volume=LWH= x(30-2x)^2
take the derivative, and set to zero.
dV/dx=0= you do it. Solve for x
Given a 30cm by 30cm sheet of metal has squares of side x cm cut from each corner. Calc. the dimension for the greatest volume.
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