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Cubes

Investigate the number of faces you can see when you arrange three cubes in different ways.

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The Big Cheese

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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Wrapping Presents

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Well, we're often wrapping up presents - I find that many of them arrive in boxes that are cuboid. Remember those? A cuboid has 6 faces; each face a rectangle (including squares); each face paired with one the same on the opposite side and all the angles 90 degrees. So they might look like these:

3cuboids

Now let's talk about the wrapping paper. You are probably used to using A4 paper for all kinds of things. A4 paper looks a bit like this:


A4Rectangle
But two A4s together make A3:



2A4's
So we have:

SimpleA3
Which could look better as:

A3withPatt
Now for easiness we'll approximate the size of the A3 sheet to 40cm by 30cm.

The wrapping paper we'll be using is A3-size, like the picture above.

So, we're wrapping up a cuboid in this A3 wrapping paper.
The challenge is to find the largest cuboid that can be covered completely with the A3 sheet - you will probably want to stick to whole numbers of centimetres!
Rather than wrapping the cuboid like we might do a birthday present, let's think about it as if we're trying to have as little overlap as possible.

You might do this practically or you may use diagrams or even a spreadsheet - it is up to you.