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