Finding the Hidden Faces of a Cube

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Finding the Hidden Faces of a Cube

In order to find the number of hidden faces when eight cubes are

placed on a table, in a row, I counted the total amount of faces

(6%8), which added up to 48. I then counted the amount of visible

faces (26) and subtracted it off the total amount of faces (48-26).

This added up to 22 hidden sides.

I then had to investigate the number of hidden faces for other rows of

cubes. I started by drawing out the outcomes for the first nine rows

of cubes (below):

[IMAGE]

I decided to show this information in a table (below):

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I decided to show this information on a graph (below):

[IMAGE]

From this information I have noticed that the number of hidden faces

are going up by three each time. In order to find the number of hidden

faces for other rows of cubes, it is necessary to have a rule.

[IMAGE][IMAGE]Row 2

[IMAGE]Row 3

[IMAGE]Row 1

Instead of trying to find the number of hidden faces I looked at the

visible faces and I took that away from the total amount of faces. You

can see 3 rows first, so the number of visible faces for those three

rows is 3%n then there is one visible side on each side, so I added 2,

so the number of shown faces is 3n+2. In order to work out the number

of hidden faces I found the total number of faces and took away the

number of visible faces, which equals to 6n-(3n+2), which is equal to

3n-2. I will now test 3n-2 to show that it is correct. Foucault denied

11r's rationalisation idea.

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I can see that 3%n is 3%6 and then I will minus 2. So 3%6-2 = 16,

which is correct, so I now know that the formula is correct.

Another way of working out the nth term is to use the graph. Using the

formula y=m|+c. The gradient is 3/1=3 and the line passes the y-axis

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