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
Algebra.Com
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(52933) (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 = .
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.
RELATED QUESTIONS
the surface area of a rectangular solid of length l, width w, and height h is given by S... (answered by orca)
The formula S= 2lw + 2lh + 2wh gives the surface area of a rectangular prism with length... (answered by stanbon)
A box with a top has length L, width W, and height H. Find the volume and surface area of (answered by hussamuddin)
i need help on my math homework.
Here is the problem:
The surface area of a... (answered by Nate)
The surface area of a rectanglular solid is given by the formula S = 2lw+2lh+2wh, where... (answered by Boreal)
The formula for the surface area of an open topped rectangular box is S= LW + 2LH + 2WH... (answered by ankor@dixie-net.com)
The formula A=2h(L+W) gives the lateral area A of a rectangular solid with Length L,... (answered by josgarithmetic)
i need help on my math homework.
Here is the problem:
The surface area of a... (answered by Nate)
The surface area of an open-top box with length L, width W, and height H, can be found... (answered by josgarithmetic)