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I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm³ cubes and are painted on the outside.
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CUBES I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm³ cubes and are painted on the outside, when these smaller cubes are taken apart some are only partly painted others none at all. Here is a table showing the number of faces painted. Cube Number Cube length No. Of small cubes No. Of small cubes with 3 painted faces No. Of small cubes with 2 painted faces No. Of small cubes with 1 painted faces No. Of small cubes with 0 painted faces 2 2*2*2 8 8 0 0 0 3 3*3*3 27 8 12 6 1 4 4*4*4 64 8 24 24 8 Straight away I noticed that the number of cubes with three sides painted is always 8 as seen in the table below and this is true for all cubes except one (see exceptions). Cube Length No. Of small cubes No. Of small cubes with 3 painted faces (Y) 2*2*2 8 8 3*3*3 27 8 4*4*4 64 8 5*5*5 125 8 6*6*6 216 8 There fore the formula for this is simply Y=8 The next table will show the formula to find cubes with two sides...
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