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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.

Candy Floss

Age 14 to 16 Short Challenge Level:

Rita is making candy floss at home.

She melts a cylinder of sugar with diameter 3 cm and length 4 cm.
She then spins it into a long cylindrical strand of diameter 1 mm.

Assuming that the melting and spinning does not affect the volume of the sugar, how long is the strand of candy floss?

This problem is taken from 1000 Problems to Enjoy
You can find more short problems, arranged by curriculum topic, in our short problems collection.