Hidden Faces Geometric Investigation

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Hidden Faces Geometric Investigation

A cube a total of 6 sides, when it is places on a surface only 5 of

the 6 faces can be seen. However if you place 5 cubes side by side,

there is a total of 30 faces, but out of this 30 only 17 can be seen.

In this coursework I will be finding out the Hidden Faces Coursework

A cube a total of 6 sides, when it is places on a surface only 5 of

the 6 faces can be seen. However if you place 5 cubes side by side,

there is a total of 30 faces, but out of this 30 only 17 can be seen.

In this coursework I will be finding out the global formula for the

total number of hidden faces for any number of cubes in any way

positioned. To find this out I will be testing various numbers of

cubes in different positions. This will enable me to find out several

different formulae. Using the formulas found I will then be able to

find out the global formula. I am generating only 3 formulae to get to

the global formula.

1 row 6 faces

1 cube 1 hidden face

1 row 12 faces

2 cubes 4 hidden faces

1 row 18 faces

3 cubes 7 hidden faces

1 row 24 faces

4 cubes 10 hidden faces

1 row 30 faces

5 cubes 13 hidden faces

1 row 36 faces

6 cubes 16 hidden faces

1 row 42 faces

7 cubes 19 hidden faces

1 row 48 faces

8 cubes 22 hidden faces

From the cubes drawn above I can see a pattern being formed. The

number of hidden faces goes up by 3 every time a cube is added on the

end.

Cubes in a row Total faces Faces seen Faces unseen

1x1 6 5 1

1x2 12 8 4

1x3 18 11 7

1x4 24 14 10

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