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.
problem
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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 ?
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.
list
Perimeter and Area
Age
14 to 16
Challenge level
This selection of problems challenges students to use their understanding of perimeter and area of shapes made from circles.
list
Surface Area and Volume
Age
14 to 16
Challenge level
This selection of problems challenges students to use their understanding of surface area and volume of three dimensional shapes based on circles.
Image
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.