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A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

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According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

The Genie in the Jar

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?

Sending a Parcel

Age 11 to 14
Challenge Level


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

This printable worksheet may be useful: Sending a Parcel.

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.