Surface area: 2Lh+2Wh+LW
volume=Lhw or h= 6912/Lw
surface area=2L(6912)/Lw+2w*6912/Lw + Lw
= 2*6912/w+2*6912/L+Lw
now, it has a square base (I just saw that, so L=W)
=2*6912/x+2*6912/x+x^2
take the derivative of area /dx
set to zero.
0=-4*6912/x^2+2x
or x^3=8(6912)
L=W=38.0976 inch
solve for h now h=6912/Lw
A box with a square base and no top is to be built with a volume of
6912 in^3. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum?
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