problem
Salinon
Age
14 to 16
Challenge level
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
Curvy areas
Age
14 to 16
Challenge level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Track design
Age
14 to 16
Challenge level
Where should runners start the 200m race so that they have all run the same distance by the finish?
problem
Arclets
Age
14 to 16
Challenge level
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
Triangles and petals
Age
14 to 16
Challenge level
An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
different flowers?
problem
Gutter
Age
14 to 16
Challenge level
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
problem
Immersion
Age
14 to 16
Challenge level
Various solids are lowered into a beaker of water. How does the water level rise in each case?
problem
Fill me up too
Age
14 to 16
Challenge level
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
Funnel
Age
14 to 16
Challenge level
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 ?