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

Teenagers and Computers Data And Statistics Project

Extracts from this document...

Introduction

image00.png

The Big Red Painted Cube Project

By

Ruth Sutton

Contents

  1. Introduction  to Part 1 The Big Painted Red Cube
  1. Cube Tables
  1. Explanation of why there isn’t a length of 1
  1. Predictions for lengths 6
  1. Explanation of the 10 x 10 x 10 cube
  1. Formula explanation
  1. The 10 x 10 x 10 table
  1. Introduction to Part 2  The Big Painted Red Cube
  1. How the cuboid works for the 5 x 4 x 3
  1. Another “ examples
  1. Formula Explanation
  1. Explanation of how a Cuboid Formula turns into the Cube Formula
  1. Introduction to Part One The Big Painted Red Cube.

A stage set for a magic act has as one prop a large cube measuring 10 feet by 10 feet by 10 feet. It is made up of a lot of little yellow cubes each 1foot in length attached together, all together there was 1000 cubes.

The big cube was dipped into a pot of red paint, and was then suspended from the ceiling on a cord, unfortunately the cord broke and it came crashing down breaking up into all the little cubes which all came apart. Matt the stage hand was given the job of collecting them all up. He noticed that some were all yellow then some had 1 red face, some had 2 red faces and so on. He wondered about how that had come about. Obviously this was because only the surface area was red.

  1. Cube Tables

a. 2 x 2 x 2 Cube

Number of red faces

Number of cubes

0

0

1

0

2

0

3

8

4

0

5

0

6

0

                              Total                                                                     8

b.

...read more.

Middle

5

6

0

0

1

8

27

64

1

0

6

24

54

96

2

0

12

24

36

48

3

8

8

8

8

8

4

0

0

0

0

0

5

0

0

0

0

0

6

0

0

0

0

0

Total

8

27

64

125

216

The formula I had at this point created was as follows.

Number of red faces

Formula

0

(n – 2 ) 3

1

6 [ (n – 2) 2]

2

n3 (n -2)3 – 6[(n – 2 )2] – 8

3

8

Total

n3

5. Explanation of the 10 x 10 x 10 cube

This was relatively easy to work out, the total was1000 cubes, because it was 10 x 10 x 10.

The zero face was accomplished by  taking the 2 adjacent cubes away then cubed .The actual sum was 10-2 = 8 x 8 x8 = 512.

The one face was worked out by subtracting the 2 corner cubes from each length of 10 (N) then multiplying by 6.  The actual sum was 10 – 2 = 8 x 8 = 64 x 6 = 384.

The two face sum was worked out by  10 -2 =8 x 12 = 96

The 3 face corners will always be 8

6. Formula Explanation

The first formula that I worked out was the total no of cubes, this was simple as to measure the volume of a cube is to cube the length that you have. This equaled to

n x n x n = n 3.

The second formula was for 0 faces, the formula for this was (n – 2) 3. The -2 is because there are 2 cubes adjacent to every side of the internal cubes , then it would be cubed minus the outer edged  each side of the cubes, as it is also a cube albeit a smaller one.

The third formula was for one red face, the formula for this was 6[ ( n-2) 2 ].

...read more.

Conclusion

The 3 face formula is the same as a cube as no matter what the size it will always have 8 corners no matter what size.

The total formula will be Width x Height x Length to get the volume.

12. Explanation of how a Cuboids Formula turns into the Cube Formula

The formula for o faces within a cuboid is ( L-2)(w-2)(h-2), if these were all the same length as in a cube the letters would become all the same for example N it would be (N-2)3 , this is the same formula as a cube

The formula for 1 face is  2[( w -2)(L -2)] + 2[(h –2)(L-2)] + 2[(h-2)(w-2)] ,if they were all changed to the same letter for example N it would be 2[( n -2)(n-2)] + 2[(n –2)(n-2)] + 2[(n-2)(n-2)], this would equalize to be the same as a cube ,the known formula is             6 [ (n – 2) 2].

The formula for 2 faces is 4(L-2) + 4( h-2) + 4(w-2), if these were all changed to the same letter , for example N it would look like this, 4(n-2) + 4( n-2) + 4(n-2), as in the previous formulas this also equalizes to the same as the cube formula for 2 faces which is 12( n-2).

If the formula for of total cubes is lwh within a cuboid if changed to the same letter for example n this would become n3, the same as the formula for a cube

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics 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

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. GCSE Mathematics Coursework: Statistics Project

    random number generator on the calculator to select the pupils from each Year, taking a Year at a time. For instance, in Year 7, as there are 275 pupils from which I must choose 24, I will enter into my calculator to get random numbers ranging from 0 < x ?

  2. &amp;quot;The lengths of lines are easier to guess than angles. Also, that year 11's ...

    For the year 9 line estimates, was 0.99, which means that the results are very compact compared to the mean, which shows that many pupils estimated very close to the mean, showing that the year 9's were better at estimating the line's length.

  1. Anthropometric Data

    So in this case the else is still giving a weak positive correlation. Showing the other weak and strong ellipse Prediction 3 From this information above I can predict that 'r' value with the outlier will give a fairly weak possible fit to the model.

  2. Used Cars - What main factor that affects the price of a second hand ...

    Estimating the value of a car that has an engine size that would fit in where most of the sample of cars are concentrated on scatter graph would give a reliable estimate value of the car because there is already data on the scatter graph that would suggest this value.

  1. Design an investigation to see if there is a significant relationship between the number ...

    I have chosen to use a tape measure to measure the lengths of the longest fronds. This is to limit the margin of error available whilst carrying out my experiment. The tape measure will be able to measure to an accuracy of 0.001m.

  2. Estimating the length of a line and the size of an angle.

    if they are a girl they will be better at estimating than a boy. Sampling In my sample frame I have two populations these are year 10 and year 11. In year 10 there are 246 students which 74 students are females and 172 students are males.

  1. Fantasy Football - Maths Coursework - Statistics

    I will group my data for this graph. With the information I find out from the cumulative frequency I will use it to draw box plots to compare the skew and distribution. For my sample I will use the method Random Quota.

  2. Bivariate Data Exploration

    A local used car showroom was approached, and data from all cars on their forecourt (and in the showroom) was collected. This data was taken directly from the records that the company keep for each car they attempt to sell, which meant the data was 'secondary'.

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