@frostedglass,
I'm nowhere close to 4220.
After reading it, I think we have 9 layers of cake (each 1.5 inches thick) and 6 layers of jam (each 1/4 inch thick). I also calculated with 3 layers of frosting and 3 cylinders of frosting.
The layers of cake and jam have diameter 2/3" less than 12, 10.5 and 9, so I used 11 1/3, 10 5/6 and 8 1/3 as my diameters.
For the frosting, I used layers of diameter 12, 10.5 and 9, thickness 1/3". I also did 3 cylinders for the sides. To find the areas of the cylinders, I took the areas of the layers and subtracted the area of a layer of cake within the tier. I took the height of each cylinder as 5 inches - 3 x 1.5 + 2 x .25 (3 cake layers and 2 jam layers).