First, thanks for getting the question to me ahead of time. So often I get questions right when the problem arises. By then, its too late to answer in time to be of help.
According to Corriher, in her new book BakeWise: The Hows and Whys of Successful Baking, springform pans may not actually measure the same diameter as they are labeled. The Food Lover's Companion does give the volume for a 9 ½" x 2 ½" springform as 10 cups, and a 10 ½" x 2 ½" springform as 12 cups.
If you have the pans on hand, you could just fill them with water using a measuring cup and see how much it takes, but since springform pans leak, you need to line them with something to keep the water in. To do that, just open kitchen garbage bag and put it into the pan, the same as if you were lining a pail. Let the excess drape around the outside, and then fill the bag inside the pan with water until it comes close to the top of the pan. The water will push the excess plastic out to the edges of the pan, so your measurement will be pretty close. It is probably best to do this in the sink to avoid a mess.
Alternatively, you can calculate the volume of the pans using the formula:
V= H x Π x r2
- H is the height of the pan, measured inside from the bottom to the height you would fill it;
- Π is the constant 3.1416
- and r2 is ½ the measured diameter of the pan squared.
Thus, for a pan which measures 9 ½" diameter and 2" high inside, the volume will be:
V = 2 x 3.1416 x4.75 x 4.75
V = 141.76 cu in
Since 1 US cup = 14.4375 cubic inches, the pan would hold about 9.8 cups or say 10 cups even.
If you are using a larger pan, but plan to fill it to the same depth, then you can just square the ratio of the diameters to get the scaling factor. A 12" pan will hold 1.6 times as much as a 9 ½" one [(12/9.5)2]. I actually recommend this, as it will cause less problems in terms of cooking time. If the pan is filled to the same depth, then the cooking time will remain close to the same (see Scaling Recipes).
Armed with the measured or calculated volumes of various pans, you can now scale your recipe. I recommend against scaling a recipe by more than a factor of two.
Start with the number of eggs in the recipe. In the above example of going from a 9 ½" pan to a 12" pan, if the original recipe calls for 4 eggs, then the scaled recipe will need 6.4 eggs. Now you have a problem, the 0.4 of an egg. The easiest thing to do will be to use 6 eggs, and scale everything by 1.5 instead of 1.6 . Scale the rest of the ingredients accordingly and proceed.
Just one more note, though. If you are scaling by volume, and the recipe calls for a crumb crust on the bottom of the pan, scale the ingredients for the crust by the ratio of the diameters, as above. If you don't, the crust will be too thick.
Make and bake the cheesecake following the hints in the posting How Can You Prevent a Cheesecake from Cracking?