SOLUTION: maximize the volume of a rectangular prism with surface 100.
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Question 1121564: maximize the volume of a rectangular prism with surface 100.
Found 3 solutions by rothauserc, Alan3354, ikleyn:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the rectangular prism has three sides a, b, c
:
surface area(SA) = 2ab +2bc +2ac = 100
:
volume(V) = abc
:
the rectangular prism of maximum volume is a cube, therefore
:
a = b = c
:
2a^2 +2a^2 +2a^2 = 100
:
6a^2 = 100
:
a^2 = 100/6 = 50/3
:
a = 5sqrt(2/3)
:
V = a^3 = 125 * (2/3) * sqrt(2/3) = 250/3 * sqrt(2/3) approximately 68.0414 square units
:
:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The other tutor said, "the rectangular prism of maximum volume is a cube..."
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I think that is true, but so far have not been able to prove it.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
The volume of a rectangular prism with given surface area is maximal when the prism is a cube.
For the proof of this statement see this site
https://www.math.dartmouth.edu//archive/m8f02/public_html/pauls_mws/boxeg.pdf
https://www.math.dartmouth.edu//archive/m8f02/public_html/pauls_mws/boxeg.pdf
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