Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radii.

What fraction of the volume of this can is filled with lemonade?

What fraction of the area of this regular hexagon is the shaded triangle?

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Can you work out the fraction of the larger square that is covered by the shaded area?

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Three touching circles have an interesting area between them...