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## 'Sending a Parcel' printed from http://nrich.maths.org/

### Why do this
problem?

This
problem gives practice in working with volume. It can be done
by either trial and improvement or by using spreadsheets. It is a
very good opportunity to see the value of using spreadsheets in
solving problems.

Before tackling the problem, it might be valuable to
investigate how the area of a rectangle can be maximised for a
given perimeter.

### Key questions

How can you express the girth in terms of the width and
breadth of the parcel?

How will you calculate the volume of the parcel?

How can you make the product of the width and breadth as large
as possible for a given girth?

Have you thought of using a spreadsheet to solve this?

What shaped rectangle will give the biggest area while the
perimeter stays the same?

What shaped cuboid do you think will give the biggest
volume?

### Possible extension

Learners could try

Zin Obelisk, which
is a similar problem.

### Possible support

Suggest trying

Oh!
Harry! which is a Stage 2 problem involving volume.