You may also like

problem icon

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

problem icon

Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

problem icon

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

All Wrapped Up

Age 7 to 11 Challenge Level:

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.