Perimeter, Area and Volume: Age 14-16

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.


  • 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?

  • Curvy areas
    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?

  • Arclets
    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?

  • Gutter
    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?

  • Fill Me Up Too
    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

    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 ?

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