Question

A cube has a side of 4 cm. The cube is painted red on all six sides. This cube is then cut into 125 smaller cubes. How many of these smaller cubes will have only one of their sides painted red.

Answer 1

The 4cm cube is divide into 125 smaller cubes:

That means that the 4 cm cube = 5 smaller cubes in height, width, and depth

Also, given that the 4 cm is painted red on all six side:
Only those smaller cubes that touch no outer surface will be free of red paint, thus:
27 smaller cubes have no red paint on them.
98 smaller cubes have some red paint on them.

How many of these smaller cubes will have only one side of their sides painted?
Only those smaller cubes that do not touch the edges of the 4 cm cube will have only one side painted, thus:
54 smaller cubes have only one side painted