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# Hidden faces investigation.

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Introduction

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.

Middle

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.

Conclusion

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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