• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3

# I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm cubes and are painted on the outside.

Extracts from this document...

Introduction

CUBES I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm� cubes and are painted on the outside, when these smaller cubes are taken apart some are only partly painted others none at all. Here is a table showing the number of faces painted. Cube Number Cube length No. Of small cubes No. Of small cubes with 3 painted faces No. Of small cubes with 2 painted faces No. Of small cubes with 1 painted faces No. Of small cubes with 0 painted faces 2 2*2*2 8 8 0 0 0 3 3*3*3 27 8 12 6 1 4 4*4*4 64 8 24 24 8 Straight away I noticed that the number of cubes with three sides painted is always 8 as seen in the table below and this is true for all cubes except one (see exceptions). ...read more.

Middle

then noticed that it would make sense to minus two from the cube number as for the first two cubes there aren't any cubes with two sides painted. As seen below in blue I get a matching pattern that forms the twelve times table. Simply by knowing the dimensions of a cube I can work out how many small cubes there would be with two sides painted in any cube e.g. the following: 3 -2= 1*12=12 4 -2= 2*12=24 5 -2= 3*12=36 6 -2= 4*12=48 7 -2= 5*12=60 8 -2= 6*12=72 Thus finding and proving the formula Y=(X-2)12 This table shows the number of cubes with only one side painted. Cube Number (X) Cube dimensions No. Of small cubes No. Of small cubes with 1 painted faces 2 2*2*2 8 0 3 3*3*3 27 6 4 4*4*4 64 24 5 5*5*5 125 54 6 ...read more.

Conclusion

Cube Number (X) Cube dimensions No. Of small cubes No. Of small cubes with 0 painted faces 2 2*2*2 8 0 3 3*3*3 27 1 4 4*4*4 64 8 5 5*5*5 125 27 6 6*6*6 216 64 This formula was perhaps the easiest to puzzle out, because of all the clues I have learnt to spot in previous formulas. The first thing I noticed about this is that the number of small cubes with no sides painted mirrored that of the number of total small cubes starting at eight two rows down in red, this led me to believe that a minus of two was needed in the formula. I then noticed that the number of small cubes were obviously all made up of cubed numbers so the formula should also involve this, this is what I came up with: Y= 3(x-2) 3(2-2)=0 3(3-2)=1 3(4-2)=8 3(5-2)=27 3(6-2)=64 This was the proof of this formula, corresponding to the above tables results. ...read more.

The above preview is unformatted text

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Hidden Faces and Cubes essays

1. ## An investigation to look at shapes made up of other shapes (starting with triangles, ...

Now I shall test it, just to make sure it works. So where P=14, D=4 and Q=10, Q=P/2+D-1 Ð Q=7+4-1 Ð Q=10 C And where P=16, D=6 and Q=13, Q=P/2+D-1 Ð Q=8+6-1 Ð Q=13 C And where P=16, D=9 and Q=16, Q=P/2+D-1 Ð Q=8+9-1 Ð Q=16 C As I expected,

2. ## The Painted Cube - Maths Investigations

I then have to times it by 2 because there are two of each. I then had to include 2(-4L -4W -4H +12) because after I have the area for a whole side I only need the inner part. So I take away the length, width and height cubes, which

1. ## Find 4 formulae that can work out the number of cubes in a cube ...

What we did next Before we found out the 0 face painted column were cubes numbers and with the help of Miss Elahi found the formula is (n-2)3 not sure how she got the -2 part but when we tested we found it was correct.

2. ## Investigate different sized cubes, made up of single unit rods and justify formulae for ...

in the middle of each side of the cube and one in the centre obviously there are always 6 sides to a cube so, so there are 6 5 joints, it will increase with the larger cubes. With this information I can work out the formulae 50 x 50 x

1. ## The aim of my investigation is based on the number of hidden faces and ...

Faces Faces In View 72 38 34 84 45 39 96 52 44 108 59 49 120 66 54 Both formulas equal to the above results, as does the Lego Models based on the drawn set. My discoveries through studying the first and second formula I have used have shown

2. ## Shapes Investigation I will try to find the relationship between the perimeter (in cm), ...

C P=18 and D=0 � 18-2+0=16 C This proves that (for triangles at least) the formula P-2+2D=T works. This can be rearranged to give D=(T+2-P)/2 and T= P+2D-2. I do not need to test these two new formulas, as they have simply been rearranged from the existing one, P-2+2D=T.

1. ## Maths Investigation -Painted Cubes

I looked closely for patterns throughout the numbers. I found that to find the number of cubes with three faces painted, it was always a constant number (8). I then looked for a pattern in my results to find how many cubes had two faces painted.

2. ## I am going to investigate different sized cubes, made up of single unit rods ...

I will then test my formulae by counting the rods and joints and see if they correspond with the numbers that I got with the formulae. All the results of the numbers of rods and joints will be presented in tables along with the formulae that I have identified and used.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to