SOLUTION: Consider a three dimensional parallelpiped with width W, length l, and height h, given that the surface area of this parallelpiped is equal to a fixed value S, determine the sectio

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Question 1105399: Consider a three dimensional parallelpiped with width W, length l, and height h, given that the surface area of this parallelpiped is equal to a fixed value S, determine the section of parameters W, l and h so that the parallelpiped encloses the largest volume.
Answer by ikleyn(52932) About Me  (Show Source):
You can put this solution on YOUR website!
.
At given surface area S the parallelepiped enclosed the largest volume is the cube with the sides

W = L = H = sqrt%28S%2F6%29.

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

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

written by Christian Blatter.