Hidden Faces of the Cube
Introduction: I am investigating the number of hidden faces for other
cuboids made from cubes. I will use visual representation to display
my results in the form of graphs. I will collect my results in a
table. I will start to collect my information in my table starting
with one cube and building them up into rows and different sized
cuboids. At the end of my investigation I hope to have a formula
worked out, and also I hope to be able to find the number of hidden
faces on a cuboids made up from 30 cubes.
Collecting Data: I have drawn a table to record my results. In the
first column I have the number of cubes and in the second I have the
number of hidden faces. In my table I have found the hidden faces for
every one cube put down there is one hidden face on the bottom. And if
a cube is put is put next to another there are always two hidden faces
between them.
Number Of Cubes
Number Of Hidden Faces
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1
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4
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7
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10
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13
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16
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19
What This Shows: My results show a pattern occurring. For every cube
that is added the number of hidden faces grows by three each time. I
my table the number of hidden faces are lade out in a sequence. This
will help me to find a formula so I can work out the number of hidden
faces without having to count them each time. To show how I know the
numbers are in sequence I will use my knowledge of methods of
difference.
1st 2nd 3rd 4th 5th 6th 7th
[IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE] 1 4 7 10 13 16 19
+3 +3 +3 +3 +3 +3
Number of hidden faces
[IMAGE]The Differences: In this sequence (using the number of hidden
faces from my table) the difference between them is +3.
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