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