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Dividing the Field

A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two trapeziums each of equal area. How could he do this?

Two Circles

Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?

Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

Similar Cylinders

Age 14 to 16 Short Challenge Level:

A metal cube, of side 9 cm, is melted down and recast into two similar cylinders. 

The diameters of the cylinders are 4 cm and 8 cm. 

If no metal is lost in the process, what is the volume of the smaller cylinder?

This problem is adapted from 1000 Problems to Enjoy

You can find more short problems, arranged by curriculum topic, in our short problems collection.