 # Finding the Hidden Faces of a Cube

explanatory Essay
801 words
801 words 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.

[IMAGE]

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

#### In this essay, the author

• Explains that the number of hidden numbers is going up by three each time.
• Explains that they can see that 3%n is 33%6 and then they will minus 2.
• Explains how to work out the nth term using the graph.
• Explains that from these diagrams, they can see a few patterns.
• Explains that the second number goes up by -2, which is the same as summary.
• Explains that they are going to work out a formula for working out the amount of hidden amounts.
• Explains that in order to work out the number of hidden faces of this cuboid, they will summary:
• Explains the above formula as a formula that will work for all cuboids.
• Explains that they will check the formula on a regular basis to make sure it is correct.
• Opines that an6pmoq visit coursework ee in ee fo.
• Explains that if the number of rows is 3%n then there is one visible side on each side.
• Explains how they can work out the rest of the formulas from the tables. the nth term goes up by 8 and the last number is -2 % the number of rows.
• Explains that shown faces is (4%2) %2 (the front and back) + (5%2)