Surface and surface area

problem
Four points on a cube

Age

16 to 18

Challenge level

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?
problem
Wrapping presents

Age

7 to 11

Challenge level

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
problem
The big cheese

Age

7 to 11

Challenge level

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
problem
Cubes

Age

7 to 11

Challenge level

How many faces can you see when you arrange these three cubes in different ways?
article
When the angles of a triangle don't add up to 180 degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.