Can you work out the dimensions of the three cubes?
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.
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
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.