Expert: Abe Mantell - 7/17/2009

Question
A rectangular solid is made up of 12 cubes of the same size. The exposed surface is then painted red. what fraction of the surface area of the individual cubes is red?


Answer
It depends how the cubes are oriented.

For example, if the 12 cubes are arranged to be 1 layer in height,
so we might have a 4x3x1 solid, the surface area is 2(3x4)+2(3x1)+2(4x1)
=38 square units, while the total surface area of all 12 cubes is 12*6
=72 square units.  So the fraction would be 38/72 or about 53%

If the cubes are arranged to form a 2x2x3 solid, then the surface are
is 2(2x2)+2(2x3)+2(2x3)=32 square units out of the total 72, for a ratio
of 32/72 or about 44%

Abe