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# GCSE Maths - Cargo Project

Extracts from this document...

Introduction

Boxes are waiting on the quayside to be loaded onto a ship. 27 boxes are made up into a 3 x 3 x 3 cube ready for the crane. The dockers stick labels as shown on each of the 6 exposed faces of the cube. The cube is dropped as it is being loaded and the boxes are scattered. My mission is to find how many labels have 3, 2, 1 and no labels. I should also try to find a formula for any cube size, for how to work out how many 3, 2, 1 and no labels they have.

I have decided to draw out my cubes first. I will have a different colour to represent each label amount, e.g. blue for 3 labels, red for 2, etc.

Middle

level – Birds Eye View

 3 labels 2 labels 1 label No labels

1st level – Birds Eye View2nd level – Birds Eye View

3rd level – Birds Eye View4th level – Birds Eye View

 3 labels 2 labels 1 label No labels

1st

Conclusion

The formula for no labels is

n-2³

The no labeled boxes are in the centre of the cube and cannot be spotted by looking at the outside of the box. You have to use minus 2 to show that the corners are not included and then cubed because it is the inside.

After looking carefully at my results I have found formulas for how to work out any amount of labels. I have tested these formulas on a 6 by 6 by 6 square. They worked. The edges, corners and faces a cube affected these formulas. Maybe next time I will try to work why this is.

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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