This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

Can Jo make a gym bag for her trainers from the piece of fabric she has?

What shape would fit your pens and pencils best? How can you make it?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?