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'Sending a Parcel' printed from https://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.
Possible approach
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 support
Suggest trying Oh! Harry! which is a Stage 2 problem involving volume.
Possible extension
Learners could try Zin Obelisk, which is a similar problem.