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

Royce Waters

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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Answers (1)

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Rudy Singh · 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)