![On The Edge Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-7195-icon.png?itok=FDxWw7nC)
![Track design](/sites/default/files/styles/medium/public/thumbnails/content-id-7359-icon.png?itok=SoM9Ko59)
problem
Track design
Where should runners start the 200m race so that they have all run the same distance by the finish?
![Salinon](/sites/default/files/styles/medium/public/thumbnails/content-id-2425-icon.png?itok=09ypcPQx)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-6468-icon.png?itok=BhJjQwuY)
problem
Curvy areas
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
![Fill Me Up Too](/sites/default/files/styles/medium/public/thumbnails/content-id-7499-icon.jpg?itok=tBCBnfqy)
problem
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?
![Curvy Areas Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-8001-icon.png?itok=QJqMnssC)
![Arclets](/sites/default/files/styles/medium/public/thumbnails/arclets.gif?itok=OyLIqv2Q)
problem
Arclets
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](/sites/default/files/styles/medium/public/thumbnails/content-02-11-six3-icon.gif?itok=K4YCjM-x)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-5673-icon.jpg?itok=OF1ia8c1)
problem
Gutter
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
![Immersion](/sites/default/files/styles/medium/public/thumbnails/content-id-6439-icon.gif?itok=1Ef_dxXY)
problem
Immersion
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
![Efficient Cutting Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-6831-icon.png?itok=B4B-17Rl)
![Funnel](/sites/default/files/styles/medium/public/thumbnails/content-id-5890-icon.png?itok=RyYhWbEa)
problem
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 ?
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.
![Perimeter and Area](/sites/default/files/styles/medium/public/thumbnails/content-id-9741-icon.png?itok=QH-_mPMp)
list
Perimeter and Area
This selection of problems challenges students to use their understanding of perimeter and area of shapes made from circles.
![Surface Area and Volume](/sites/default/files/styles/medium/public/thumbnails/content-id-9740-icon.jpg?itok=ifImDdN2)
list
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.
Image
![Perimeter, Area and Volume - Stage 4 STEM footer Perimeter, Area and Volume - Stage 4 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13474-STEMlogo.png?itok=nj351qzB)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.