Cube Questions

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

The no. of cubes painted in one side is 98.

VINOTH,

Yes, there are 98 cubes with some paint on them, but ...

The cudes that form the 8 corners will have paint on 3 sides, not 1 side, so you need to remove them from the total of 98 cubes ...

Now there of the remain 90 cubes, the 36 cubes that are on the edges will have paint on 2 sides, not 1 side, so you need remove them from the 90 remaining total as well.

That leaves 54 cubes with paint on only 1 side.

So, given:

- A cube that has a side of 4cm
- And the cube is painted red on all six side
- And the cube is then cut into 125 smaller cubes


The answer to the question:

"How many of these smaller cubes will have only one side of their sides painted."

Is 54.