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

Teresa Woodard

Mathematics

6 November, 21:39

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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Gretchen Holden · 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)