Spheres, cylinders and cones

  • Flight Path
    problem

    Flight Path

    Age
    16 to 18
    Challenge level
    Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
  • In a Spin
    problem

    In a Spin

    Age
    14 to 16
    Challenge level
    What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
  • Pythagoras on a Sphere
    problem

    Pythagoras on a Sphere

    Age
    16 to 18
    Challenge level
    Prove Pythagoras' Theorem for right-angled spherical triangles.
  • Spherical triangles on very big spheres
    problem

    Spherical Triangles on Very Big Spheres

    Age
    16 to 18
    Challenge level
    Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
  • Cylinder Cutting
    problem

    Cylinder Cutting

    Age
    7 to 11
    Challenge level
    An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
  • Yellow drawstring bag.
    problem

    Gym Bag

    Age
    11 to 16
    Challenge level

    Can Jo make a gym bag for her trainers from the piece of fabric she has?

  • Conical Bottle
    problem

    Conical Bottle

    Age
    14 to 16
    Challenge level

    A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

  • Three tennis balls on a clay surface.
    problem

    Three Balls

    Age
    14 to 16
    Challenge level

    Do points P and Q lie inside, on, or outside this circle?

  • Tin Tight
    problem

    Tin Tight

    Age
    14 to 16
    Challenge level

    What's the most efficient proportion for a 1 litre tin of paint?

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