SOLUTION: Can you please help me on how to minimize the surface area of a square based prism Thanks

Question 118539: Can you please help me on how to minimize the surface area of a square based prism
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume a side of the square base is x; then the area of the base is x^2
Assume the height is h.
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The surface area is top and bottom = x^2+x^2 = 2x^2
The sides area is 4(xh) = 4hx
The total area is 2x^2+4hx
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EQUATION:
Surface Area = 2x^2+4hx
This is a quadratic formula and the minimum occurs at x = -b/2a
-b/2a = (-2(4h))/4 = -2h
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The Surface area when x = -2h is as follows:
SA(-2h) = 2(-2h)^2+4h(-2h)
SA(-2h) = 2(4h^2)-8h^2
SA(-2h) = 0
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Comment: I doubt that is the answer you want by zero is
certainly a minimum surface area.
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Cheers,
Stan H.
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