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'Changing Areas, Changing Volumes' printed from http://nrich.maths.org/
Try working on Changing Areas,
first, as it is a two-dimensional version
of this three-dimensional problem.
If I know two rectangles have the same area, how can I decide, just
by looking at their dimensions, which has the greater
If I know two cuboids have the same volume, how can I decide, just
by looking at their dimensions, which has the greater surface