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Glue three cubes together to make a cuboid of dimensions 3 by 1 by 1. Label 4 points on the cuboid with coordinates A = (0,0,0), B=(1,1,1), C=(2,1,0) and D=(3,1,0). Now the challenge is to find at least two different ways to calculate the angles \angle ABC and \angle ABD.
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
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.
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?