You can put this solution on YOUR website! A box with a square bottom and no top must contain 108 cubic inches. What dimensions will minimize the surface area?
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Let x = length and width of the bottom of the box
then = the height of the box
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Surface area with no top = (L*W) + 2(L*H) + 2(W*H)
:
SA = x^2 + 2(x*) + 2(x*)
Cancel x
SA = x^2 + 2() + 2()
:
SA = x^2 + () + ()
:
SA = x^2 + ()
Graph this equation to find the min surface area for the given volume
Surface area is the y axis.
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Minimum: x = 6" is the length and the width of the bottom
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Find the Height
h = = 3" is the height
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check the volume
6 * 6 * 3 = 108 cu/in
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Interesting that the min surface area is also 108 (but sq/in)
(6*6) + 2(6*3) + 2(6*3) = 108
