Sure the ratio of the radius squares will give you a ball park answer. Differences in tire shape and wall thickness would account for any departures from theory. On the other hand the empirical method is just too easy for you not to use it. Do the experiment and see what you come up with. And don't forget you can/should use lower pressure in the wider tire, so that will help. Quite likely it is two cartridges for the larger tire, but it won't cost more than a few dollars to test for yourself. BTW, cartridges are cheap when bought in bulk from a mail order source not related to hobbies or bikes.