This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
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?
Curvy areas
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Track design
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
Gutter
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Immersion
Various solids are lowered into a beaker of water. How does the water level rise in each case?
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?
Arclets
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 ?
Perimeter and area
Surface area and volume
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.