justloveyuki9424 justloveyuki9424

28-11-2017
Mathematics

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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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naeemahmed204 naeemahmed204

28-11-2017

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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