# To investigate the hidden faces and the number of faces seen on a cube or a cuboids when it&#146;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.

This student written piece of work is one of many that can be found in our GCSE Hidden Faces and Cubes section.

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