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Volume of a Pyramid and a Cone

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.

Efficient Cutting

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.

Cola Can

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

There and Back Again

Age 11 to 14
Challenge Level

Bilbo decides to leave his hobbit-hole and go on an adventure. He walks 100 miles South, then 100 miles East, then finally 100 miles North, at which point he is surprised to find that he has arrived back home!

Many people would think that because of this Bilbo must live at the North Pole.
However, Bilbo doesn't live at the North Pole!

Can you describe where you think his home might be?
Have you found all the possible locations?