The 4cm cube is divide into 125 smaller cubes:
that means that the 4cm cube = 5 smaller cubes in height, width, and depth
Also, given that the 4cm 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 4cm cube will have only one side painted, thus:
- 54 smaller cubes have only one side painted
- 36 smaller cubes have two sides painted
- 8 smaller cubes have three sides painted