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To investigate the hidden faces and the number of faces seen on a cube or a cuboids when it’s placed on a table.

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Introduction

Cubes Aim: To investigate the hidden faces and the number of faces seen on a cube or a cuboids when it's placed on a table. Introduction: My task is to find out the hidden faces and the number of faces seen on a cube or cuboids. When a cube is placed on a table only 5 of the faces can be seen. So 1 face is hidden. Here are the tables and results we did to find out the over all formula: 1) Number of cubes (x) Hidden faces Number of faces seen Total faces 1 1 5 6 2 4 8 12 3 7 11 18 4 10 14 24 5 13 17 30 10 28 32 60 15 43 47 90 20 57 63 120 x= number of cubes 3x+2= Number of faces seen These are the 3 faces seen they are same for each cube in the row, that's why I multiplied it by 3. ...read more.

Middle

We put the results in a table and found out that the hidden faces went up by 2 when we increased the number of cubes. The 1st investigation went up by 3 and so the 1st ones formula was multiplied by 3 so I thought this one was multiplied by 2 and I minus 1 because there was only one side which we could see. 3) Number of cubes (x) Hidden faces Number of faces seen Total faces 4 12 12 24 6 20 16 36 8 28 20 48 4x-4=Hidden faces You multiply it by 4 because you can see 4 faces, I minus 4 faces because you can see 4 sides but I took this as if I couldn't see. 2x+4=number of faces seen. I multiplied it by 2 because the numbers of cubes are going in 2's so we add 4 because you can see 4 sides. ...read more.

Conclusion

I have found out the overall formula for a cube and cuboids because it was linked to volume and surface area. The overall formula for the number of faces seen is, L�W+(H�L)�2+(H�W)�2 And the formula to find out the hidden faces is, L�W�H�6-Number of faces seen. Number of faces seen= (L�W) + (H�L) �2+ (H�W) �2 Hidden faces= L�W�H�6-Number of faces seen. Here are some examples to prove that my formula works. This formula works with a cubes and cuboids. There is only one variable, because if we had more than 1 variable than it would be hard to find out the link between each variable. If I was to carry on I would change the shapes in to a different shape or to investigate the different patterns that occur with different cubes and cuboids when all the faces are painted of a large cube or a cuboids and then that is separated into smaller cubes and then how many faces of each small cube are still painted. ...read more.

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