problem

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### Salinon

This shape comprises four semi-circles. What is the relationship
between the area of the shaded region and the area of the circle on
AB as diameter?

problem

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### Curvy areas

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

problem

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### Track design

Where should runners start the 200m race so that they have all run the same distance by the finish?

problem

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### Arclets

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

problem

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### Triangles and petals

An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
different flowers?

problem

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### Gutter

Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?

problem

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### Immersion

Various solids are lowered into a beaker of water. How does the
water level rise in each case?

problem

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### Fill Me Up Too

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

problem

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### Funnel

A plastic funnel is used to pour liquids through narrow apertures.
What shape funnel would use the least amount of plastic to
manufacture for any specific volume ?