CUBES: Painted Faces: INVESTIGATION

This investigation is about a cube made out of smaller cubes. The large cube has been painted. In the investigation I am going to look at the relationships between the size of the large cube and the number of painted faces each smaller cube has.

KEY:
Small cube has 3 painted sides

Small cube has 2 painted sides

Small cube has 1 painted side




In this cube, there are 64 SMALLER CUBES.

That means…
8 CUBES with 3 painted sides.
24 CUBES with 2 painted sides.
16 CUBES with 1 painted side.
16 CUBES with 0 painted side.

There isn’t much we can conclude from these results until we have seen another cube. Here is a 5x5 cube.

In this cube, there are
125 SMALLER CUBES.

That means…
8 CUBES with 3 painted sides.
36 CUBES with 2 painted sides.
54 CUBES with 1 painted side.
27 CUBES with 0 painted sides.




From this cube, and the 4x4 cube before, we can make some conclusions. Firstly, that the number of cubes with 3 painted sides will always be 8. Secondly, that the number of cubes with 1 painted side is the number of 1-painted cubes on 1 side, multiplied by six. [EG on one side of a cube there are 6 1-painted cubes, so in the whole cube there will be 36.]

To find out the relationship between the numbers of cubes with 2 painted sides, we should look at a 6x6 cube.