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20 September, 18:04

A box has a bottom with one edge 8 times as long as the other. if the box has no top and the volume is fixed at v, what dimensions minimize the surface area?

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  1. 20 September, 20:08
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    height: h=V/w / (9w) = V / (9w^2)

    surface area: w*9w + h * (20w) = 9w^2 + 20wV / (9w^2) = 9w^2 + 20/9 V/w

    minimum at:

    w = cube root of (10/81 V)

    dimensions:

    w, 9w, V / (9w^2)
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