9-inch Round Cake Pan
Using the formula of the cylinder, a 9-inch cake pan that is 1 inch high will hold a volume of about 6358 cubic inches. At 144 cubic inches to the cup, that's 44 cups.
You can get the volume of higher pans by multiplying that volume by the number of inches for the height. Thus, a 15-inch pan would have a volume of 66 cups, and a 2-inch pan would be 88 cups.
10-inch Round Cake Pan
The 10-inch round cake pan may not seem much bigger, but its volume exceeds the volume of a 9-inch pan significantly. The 10-inch pan, 1-inch high holds about 785 cubic inches.
That translates to 545 cups. Similarly, to get volumes for a 15- or 2-inch pans, multiply by 15 or 2 respectively.
This yields volumes of 8175 and 109 cups.
You will probably not be filling the pans to the brim, if you are doing some baking rather than using volume measurements for a science project. For fills that are a portion of the full depth of the pan, multiply the amount by the factor for the depth.
For example, a fill of two-thirds on a pan with a volume of 109 cups would be 109 times 067, or 73 cups.
For baking replacement purposes, should you not have a pan of the required size for your recipe, you can use pans of other shapes instead. A 9-inch round pan that is 15-inches high can be used instead of a 8-inch x 4-inch rectangular loaf pan, or a 7-inch by 11-inch baking pan, and vice versa.
Your 10-inch pan with a 15-inch height can be used in place of two 8-inch round pans. If the depth of the batter fill differs significantly, baking time can be altered.
The deeper fills require more time.