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Hidden Faces.

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Introduction

HIDDEN FACES

Hidden Faces: Hidden faces are those hidden after the cubes have been viewed from all angles.

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.

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Middle

Number of hidden faces

image05.pngThe Differences: In this sequence (using the number of hidden faces from my table) the difference between them is +3. So what ever my formula turns out to be it must have a 3 in it. If I use 'N' as representing the number of cubes. My formula looks like this '3N' or 3xN. So If a number of cubes are put into my formula it will go through like this.

Number of cubes

3

X =

image06.png




Prediction: I predict that if I put a 9 and then a 7 into my formula. 9 cubes will have 27 hidden faces. And if I put 7 cubes into my formula there will be 21 hidden faces.

The Final Piece: If I put a 9 into my formula it gives me 3x9=27. And if I put a 7 in it will come out like this 3x7 =21. So my prediction was right but if you count the number of hidden faces without using the formula 9 cubes has 25 hidden faces and 7 cubes has 19 hidden faces. So each time the number of hidden faces is -2 more than I predicted.

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Conclusion

18 cubes stacked = 3.5 x 18 = 63

So my formula so far is wrong. Because each time I put in a number of cubes the number of hidden faces is four more than I predicted. Each time I am having to - 4 each time to get the right number of hidden faces. My formula is now complete and looks like this 3.5n - 4.To prove this I am going to input different amounts of cubes.

26 stacked cubes = 3.5 x 26 = 91

91 - 4 = 86 hidden faces

30 stacked cubes = 3.5 x 30 = 105

105 - 4 = 101 hidden faces

36 stacked cubes = 3.5 x 36 = 126

126 - 4 = 122 hidden faces

So my second formula also works. My second way of working it out like I did for cubes in a row which is 6n - S this also works using stacked cubes

Conclusion: In conclusion my investigation shows how my formulas help to find the number of hidden faces. My first formula works only for cubes in a row. My second formula only works for cubes stacked two high in a line. But the amazing thing is that the formula that works for both is the other way of working out the number of hidden faces 6n- S. This formula involves a lot more working out but can be effective if used.

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