Find 4 formulae that can work out the number of cubes in a cube that has been painted on the outside with 0 faces painted, 1 face painted, 2 faces painted and 3 faces painted in any sized cubes.

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Math’s Painted Cube Investigation

Aim: Our aim is to find 4 formulae that can work out the number of cubes in a cube that has been painted on the outside with 0 faces painted, 1 face painted, 2 faces painted and 3 faces painted in any sized cubes.

Method:

1. We drew out all the different sizes of cubes up to 5x5 like the following:

1x1 cube            

       

2x2 Cube

3x3 Cube

4x4 Cube

 

5x5 Cube

2. Then counted how many with 1 face painted and imagine the ones that were not shown.

3. The counted how many 2 faces painted and imagine the ones which are not shown.

3.The counted the faces painted and imagined the ones that are not shown.

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4. Next we recorded our results in a results table.

4. We then found formulae for them.

Results:

All results were recorded in a table, so if a pattern were to occur, it would be easier to spot.

Next we tried to see if there was a pattern like square numbers, cube numbers, triangular numbers, odd numbers or even numbers.  

We found out the following:

0 Face: 0,0,1,8,27 (Tasneem with the help of the revision guide found out that these numbers were cube numbers).

1 Face:0, 0,6,24,54 (Asma found out these numbers were ...

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