Who didn't pay attention in maths classes then?
;-)
Assuming that you keep the height of the cake the same, you'll double its volume (giving you twice as much cake) by multiplying its diameter by the square root of 2, so you'll require a 10" cake tin.
If you want the cake to be the same shape as the one in the recipe (i.e. it will be higher, as well as wider) you need to multiply the dimensions by the cube root of 2, so you'll require a 9" cake tin.
If you buy a 14" cake tin (but keep the height the same) you'll end up with 4 times as much cake or, if you also double its height, you'll have 8 times as much cake.