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Introduction

Maths Coursework - Hidden Faces

Part 1

Part 1 was the first investigation which required me to investigate the number of hidden faces for rows of cubes. I must show progress and predictions while carrying out the investigation to find a relationship between the numbers of faces shown depending on the number of cubes. For example when you have one cube there are six faces and one hidden face and if you join up another cube on to it the number of faces double and calculates to for hidden faces. My aim is to come up with a formula that will enable me to calculate the amount of hidden faces without counting them.

The sheet shows this as an example.

Middle

6

5

1

2

12

8

4

3

18

11

7

4

24

14

10

5

30

17

13

The table is showing here that when a cube is added the number of sides goes up by 6, the seen faces go up by 3 and then hidden faces goes up by 3. This pattern now helped me predict the next two cubes 6 and 7. To see my predictions look below.

 Cube Number of sides Seen faces Hidden faces 6 36 20 16 7 42 23 19

Soon after the predictions I made I thought I could come up with a simple rule which

Conclusion

E.G. 5 cubes = 17 seen faces – 4 = 13 hidden faces

6 cubes = 20 seen faces – 4 = 16 hidden faces

There is a pattern emerging of – 3

Soon after all these predictions I then went on to write out my rule. The rule that I came out with was: This rule was consistent and worked as you can see :

1 cube x 3 = 3 – 2 = 1

2 cubes x 3 = 6 – 2 = 4

3 cubes x 3 = 9 – 2 = 7

Here was part of the table made which I collected the results which I counted myself using 3D cubes.

 Cube Number of sides Seen faces Hidden faces 1 6 5 1 2 12 8 4 3 18 11 7

As you can see the results came up correct. That’s the end of investigation 1

Part 2

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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