Maths Project : Cubes and Hidden Faces

3X1=3 and I need 1

3X2=6 and I need 4

3X3=9 and I need 7

3X4=12 and I need 10

It looks like that I have to-2 to get the numbers I want so the nth term is 3n-2. To find the 100 you time 3 by 100 and-4 which = 296

Using this nth term I have made a table with out having to draw all of the pictures.

Number of cubes

Number of hidden faces

2

4

3

7

4

0

5

3

6

6

7

9

8

22

9

25

0

28

1

31

2

34

3

37

4

40

5

43

6

46

7

49

8

52

9

55

20

58

Hidden Faces Part 2

I am still looking for the pattern but this time using different shapes.

2 cubes = 4 hidden faces.

4 cubes = 12 hidden faces

6 cubes = 20 hidden Faces

8 cubes = 28 hidden faces

This time the pattern goes up in 8 and I will now find the nth term.

st 2nd 3rd 4th

4 12 20 28

8 8 8

8X1= 8 and I need 4

8X2= 16 and I need 12

8X3= 24 and I need 20

8X4= 32 and I need 28

From this I can see that I need to - 4 so the nth term is 8n-4. to find the 100 number of hidden faces times 8 by 100 and -4 which = 796

Now I can draw a table of results with out drawing all the pictures.

Number of cubes

Number of hidden faces

2

4

4

2

6

20

8

28

0

36

2

44

4

52

8

60

20

68

22

76

24

84

26

92

28

00

30

08

32

16

34

24

38

32

40

40

42

48

44

56

Hidden Faces Part 3

Now I will be drawing the shapes as above but I will be putting it on its side to see if that will change the results.

2 Cubes = 3 hidden faces

4 cubes = 10 hidden faces

6 cubes = 17 Hidden faces

8 cubes = 24 hidden faces

10 cubes = 31 hidden faces

I will now work out the nth term.

1st 2nd 3rd 4th 5th

3 10 17 24 31

7 7 7 7

7X1= 7 and I need 3

7X2= 14 and I need 10

7X3= 21 and I need 17

7X4= 28 and I need 24

7X5= 35 and I need 31

I need to - 4 to get the right number so the nth term is 7n-4. To get the number for 100 cubes I will times 7 by 100 and - 4 to get 696. I can now draw a table of results.

Number of cubes

Number of hidden faces

2

3

4

0

6

7

8

24

0

31

2

38

4

45

6

52

8

59

20

66

22

73

24

80

26

87

28

94

30

01

32

08

34

15

36

22

38

29

Jamie Moore 02/05/07