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Very interesting solution.

Measure the Length, Width, and Height.

Volume = L W H

Area = 2LW + 2LH + 2WH

Ratio of (Area)/(Volume) = (2LW + 2LH + 2WH) / (L W H) = ( 2 / H ) + ( 2 / W ) + ( 2 / L )

I never knew that ! It works for any rectangular box.

-- Take the reciprocals of Length, Width, and Height.
-- Sum the reciprocals.
-- Double the sum is the ratio of the box's area to its volume.

The minimum ratio .... i.e. the box that holds the most volume in the least cardboard ...
is a cube, for which the ratio is '6'.

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