As I recall, baking a cake until it is done has no relationship to the shape of the pan, but whether the cake is finishing cooking or not. It is the cake that you want to concern yourself with, not the pan. And that is usually determined by testing the very center of the cake (the part farthest away fron the edge) with a tooth pick or skewer and seeing whether it comes out cleanly or has raw batter clinging to it. Once it tests clean, the cake is done. Enjoy your cake.
Never trust a skinny chef!