Find the shape and symmetries of the two pieces of this cut cube.
What is the surface area of the tetrahedron with one vertex at O
the vertex of a unit cube and the other vertices at the centres of
the faces of the cube not containing O?
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.
A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.