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Colourful Cube

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Student Solutions
  • Teachers' Resources

This printable worksheet may be useful: Colourful Cube.

This problem has not yet got Teachers' Notes.

If you have used this problem in your classroom, and would like to share your approach and your experiences with other teachers, please email us at secondary.nrich@maths.org

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Boxed In

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

Plutarch's Boxes

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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