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?

Question

Mathematics

Karson Huff

24 December, 09:25

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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Answers (1)

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London Monroe · Answer 1

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)