All Wrapped Up

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:



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:



But two A4s together make A3:




So we have:


Which could look better as:


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.