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?
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?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Find the shape and symmetries of the two pieces of this cut cube.