Spheres, cylinders and cones

problem

Air Routes

Age

16 to 18

Challenge level

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
problem

Flight Path

Age

16 to 18

Challenge level

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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?
problem

Peeling the Apple or the Cone That Lost Its Head

Age

14 to 16

Challenge level

How much peel does an apple have?
problem

Pythagoras on a Sphere

Age

16 to 18

Challenge level

Prove Pythagoras' Theorem for right-angled spherical triangles.
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.
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.
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?
problem

Three Balls

Age

14 to 16

Challenge level

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

Tin Tight

Age

14 to 16

Challenge level

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