If a cube that is 5cm x 6cm x 6cm is covered in wax then cut up into 1 cm cubes. How many cubes will have at least one side covered by wax?
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There are 180=6*6*5 cubes in all. To find out how many cubes will have no wax at all, reduce the sides of the large cuboid (rectangular prism) by two cubes for each face. This will leave a core of cubes 4*4*3=48. These cubes will not be covered in wax. So the remaining 180-48=132 cubes will have at least one face covered by wax.

(It may help to think of a cube side 3. This contains 27 unit cubes, but only the central cube is unexposed and (3-2)^3=1. The dimensions of the faces are each reduced by 2.)

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