Question

In a small town called Edam, cheese is given a perfect spherical shape of radius 100 milimeters, and covered with a thin layer of red wax. When the locals sliced the cheese, and melted the wax of each slice, they found out, to their amazement, that they got the same amount of wax, no matter where they cut the cheese. (No pun intended). Show that if you cut a slice of that cheese of thickness T, the external area of the wax is proportional to T (that is, a constant times T), henceforth, showing that the surface area of a slice of a sphere is independent of the position of the slice with respect to its center.

Answer 1