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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Conical Bottle

Age 14 to 16 Challenge Level:

A right circular cone is filled with liquid to a depth of half its vertical height.

The cone is inverted. How high up the vertical height of the cone will the liquid rise?