Volume and capacity

  • Cuboid challenge
    problem
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    Cuboid Challenge

    Age
    11 to 16
    Challenge level

    What's the largest volume of box you can make from a square of paper?

  • Three cubes
    problem
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    Three Cubes

    Age
    14 to 16
    Challenge level

    Can you work out the dimensions of the three cubes?

  • problem
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    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
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    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
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    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 ?

  • Plane to See
    problem

    Plane to See

    Age
    16 to 18
    Challenge level
    P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
  • Reach for Polydron
    problem

    Reach for Polydron

    Age
    16 to 18
    Challenge level
    A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.
  • Concrete calculation
    problem

    Concrete Calculation

    Age
    14 to 16
    Challenge level
    The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?
  • Sliced
    problem

    Sliced

    Age
    14 to 16
    Challenge level
    An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?
  • Maths filler 2
    problem

    Maths Filler 2

    Age
    14 to 16
    Challenge level
    Can you draw the height-time chart as this complicated vessel fills with water?
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