The cylinder $\displaystyle x^2 + y^2=1$ divides the sphere $\displaystyle x^2+y^2+z^2=36$ into two regions $\displaystyle I$ (for the region inside the cylinder), and $\displaystyle O$ (for the region outside the cylinder). Find the ratio of the areas $\displaystyle A(O)/A(I)$.

It's really complicated and I can't figure out where to start! Help!