Can you work out the dimensions of the three cubes?
Which of the following cubes can be made from these nets?
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.
This is a nice activity to take slowly and build up
understanding in each part.
It also makes a nice lead in towards maths at the next level,
especially if the spreadsheet is used to improve accuracy as each
fustum height becomes smaller without limit.