Question 1105399
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At given surface area S the parallelepiped enclosed the largest volume is the cube with the sides 


W = L = H = {{{sqrt(S/6)}}}.


For very short and straightforward derivation/proof of this fact see the text under the link


<A HREF=https://math.stackexchange.com/questions/2428174/rectangular-parallelepiped-of-greatest-volume-for-a-given-surface-area-s>https://math.stackexchange.com/questions/2428174/rectangular-parallelepiped-of-greatest-volume-for-a-given-surface-area-s</A>


https://math.stackexchange.com/questions/2428174/rectangular-parallelepiped-of-greatest-volume-for-a-given-surface-area-s


written by Christian Blatter.