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Hidden faces investigation.

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Hidden Faces Investigation Introduction I am going to investigate the number of hidden faces when cubes are joined together. The aim of this task is to find a formula, which is common with every cube and hidden face. I will be using multi-link for this investigation. First I will see how many hidden faces are on 1 cube and carry on until I reach up to 6 cubes. One cube has one hidden face and it is the one that is on the table. When there is more than one cube there will also be 2 or more hidden faces where they join together. Hidden Face is here underneath the cube, the face that is on the table. Prediction I predict that with 1 cube there will be 1 hidden face and this face is faced down to the table, but because I have to add cubes to the row each time the number of hidden faces will increase, so will the showing faces and the faces altogether. ...read more.


These 4 cubes have a total of 12 hidden faces. Eight of the hidden faces are where they are all joined together, the other 4 are underneath where they are facing down onto the table. 12 faces hidden 12 faces showing 24 faces altogether I have found out that the number of hidden faces goes up in 8's so my first formula won't work with this part. There is another formula that I have found that works with this part, it is 8n - 4. Number of cubes Number of faces showing Number of hidden faces 2 4 6 8 10 12 8 12 16 20 24 28 4 12 20 28 36 44 I predict that 14 cubes will have 52 hidden faces because 8 x 7 = 56 and you then use the formula which is 8n - 4 and 56 - 4 = 52 so that's how I get my prediction. I am now going to investigate a 30 cube cuboid. I will find out the number of hidden faces then count the hidden faces row by row, by doing this I will be able to work out the formula for 30 cubes. ...read more.


Overall Conclusion By looking at my previous investigation looking at the amount of hidden faces in cuboids, I have came across many different formulas and patterns for the first investigation, I used one row of cubes I found a pattern and worked out the formula to be 3n - 2. then I went onto my second investigation I used two rows going up joining together I gathered some results and put it into a table I tried my first formula on the second lot of results but it didn't work. I found the formula to be 8n - 4. I found the second part much more complicated than the first part. Then I went onto a 30 cube cuboid I found this very hard to work out but I realised the formula was right in front of me I realised there was 6 faces to a cube and I was using 30 cubes so I done 6 x 30 which worked out to be 180 then I counted the number of faces showing which was 47 I subtracted this from 180 to be 133 used another method and I came out with the same answer. Stuart Pelling GCSE Mathematics coursework Page 4 ...read more.

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