An enormous baloney slicer is heading towards Earth. The baloney slicer is essentially an enormous fence of infinitely sharp wires, spaced an inch apart, and both wide enough and high enough to handle the Earth.
For convenience, let's say that when the baloney slicer and the Earth hit, they are "parallel", that is, that the North Pole just glides under the first wire in the grid, the South Pole just scrapes over the last wire in the grid. This means, for instance, that lines of latitude are parallel to the wires.
Now that the Earth is a stack of one inch slices, it's obvious that the slices at the Equator are the most massive. But that's not important to us. We live on the surface of the Earth, so the important question concerns the surface area of the slices: what is the relationship between the surface areas of a slice at the Equator, at the 45 degree latitude line, and the topmost slice that includes the North Pole?
I give up, show me the solution.