Find the shape and symmetries of the two pieces of this cut cube.
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?
Take a cube of side length one unit. A vertex of the cube and
the centres of the three faces not containing that vertex form the
vertices of a tetrahedron. What is the surface area of this