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Maths Project : Cubes and Hidden Faces

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Introduction

Maths Project : Cubes and Hidden Faces I am finding out if there is a pattern to the ratio of cubes to the number of hidden faces and finding the nth term. With 1 Cube = 1 hidden face With 2 Cubes = 4 hidden faces With 3 Cubes = 7 hidden faces With 4 Cubes = 10 hidden faces With 5 Cubes = 13 hidden faces With 6 Cubes = 16 hidden faces Already I can see a pattern, which is that with each cube, added there are 3 more hidden faces. Now I will try to find the nth term. 1st 2nd 3rd 4th 5th 6th 1 4 7 10 13 16 3 3 3 3 3 3X1=3 and I need 1 3X2=6 ...read more.

Middle

2 cubes = 4 hidden faces. 4 cubes = 12 hidden faces 6 cubes = 20 hidden Faces 8 cubes = 28 hidden faces This time the pattern goes up in 8 and I will now find the nth term. 1st 2nd 3rd 4th 4 12 20 28 8 8 8 8X1= 8 and I need 4 8X2= 16 and I need 12 8X3= 24 and I need 20 8X4= 32 and I need 28 From this I can see that I need to - 4 so the nth term is 8n-4. to find the 100 number of hidden faces times 8 by 100 and -4 which = 796 Now I can draw a table of results with out drawing all the pictures. ...read more.

Conclusion

1st 2nd 3rd 4th 5th 3 10 17 24 31 7 7 7 7 7X1= 7 and I need 3 7X2= 14 and I need 10 7X3= 21 and I need 17 7X4= 28 and I need 24 7X5= 35 and I need 31 I need to - 4 to get the right number so the nth term is 7n-4. To get the number for 100 cubes I will times 7 by 100 and - 4 to get 696. I can now draw a table of results. Number of cubes Number of hidden faces 2 3 4 10 6 17 8 24 10 31 12 38 14 45 16 52 18 59 20 66 22 73 24 80 26 87 28 94 30 101 32 108 34 115 36 122 38 129 Jamie Moore 02/05/07 1 ...read more.

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