Holojg

Cubes coursework.

Aim: To find out the general formula for cubes with the same sized sides.
Hypothesis: if all the sides go up by 1 each time then the results will have a drastic change betweenthem.
Method:
1. With dotted paper start by drawing a cube that is 3x3x3 cubes.
2. Draw a cube that is 4x4x4 cubes.
3. Draw another cube that is 5x5x5
4. Draw one last cube that is6x6x6.
5. Colour with any colours you want the cubes that have 1 faces painted, 2 faces painted and 3 faces painted. Labe label one as “A” another as “B” and the last one as “C” there is one type ofcube that has no faces painted. Label this one as “D”.
6. For all of the cubes count how many 1 faced painted cubes there is, how many 2 faced painted cubes there is, how many 3 faced paintedcubes there is and finally how many no faced painted cubes there is.
7. After doing step 6 plot a graph like this and fill in the results in it.
n-2 | w | l | n | a | b | c | d |
1 | 3 | 3 | 3 || | | |
2 | 4 | 4 | 4 | | | | |
3 | 5 | 5 | 5 | | | | |
4 | 6 | 6 | 6 | | | | |
8. Fill this table with the results you got from “A”, “B”, “C” and “D”.
9. After doing thisyou will have ended with something like this:
n-2 | w | l | n | a | b | c | d |
1 | 3 | 3 | 3 | 6 | 8 | 12 | 1 |
2 | 4 | 4 | 4 | 24 | 8 | 24 | 8 |
3 | 5 | 5 | 5 | 54 | 8 | 36 | 27 |
4 | 6 |6 | 6 | 96 | 8 | 48 | 64 |
10. After this get the pattern of each one of these patterns. After you have done this you can start getting the general formula.

w | h | l | A | B | C | D |
3| 3 | 4 | 10 | 8 | 16 | 2 |
3 | 3 | 5 | 14 | 8 | 20 | 3 |
3 | 3 | 6 | 18 | 8 | 24 | 4 |
3 | 3 | 7 | 22 | 8 | 28 | 5 |
3 | 3 | 8 | 26 | 8 | 32 | 6 |
3 | 3 | 9 | 30 | 8 | 36 | 7 |

w | h |l | A | B | C | D |
3 | 4 | 3 | 10 | 8 | 16 | 2 |
3 | 4 | 4 | 16 | 8 | 20 | 4 |
3 | 4 | 5 | 22 | 8 | 24 | 6 |
3 | 4 | 6 | 28 | 8 | 28 | 8 |
3 | 4 | 7 | 34 | 8 | 32 | 10 |

w | h | l | A...