Age 14 to 16
Challenge Level
Perimeter and Area
This selection of problems challenges students to use their understanding of perimeter and area of shapes made from circles.
Age 14 to 16
Challenge Level
Surface Area and Volume
This selection of problems challenges students to use their understanding of surface area and volume of three dimensional shapes based on circles.
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?
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?
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?
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".
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?
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?
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?
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?
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 ?
Perimeter, Area and Volume Short Problems
Age 11 to 16
A collection of short problems on area and volume.
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.
NRICH is part of the family of activities in the Millennium Mathematics Project.