The volume calculation for a 9-inch or 10-inch round cake pan is a basic geometric formula. Since the pans are cylinders, albeit short ones, by squaring the radius of the pan, this being half the diameter, then multiplying by 3.14 (or pi) you get the area of the base of the pan. Multiply that by the height, and you have the volume. That volume will be in cubic inches, so convert it cups for cooking purposes.
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 63.58 cubic inches. At 14.4 cubic inches to the cup, that's 4.4 cups. You can get the volume of higher pans by multiplying that volume by the number of inches for the height. Thus, a 1.5-inch pan would have a volume of 6.6 cups, and a 2-inch pan would be 8.8 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 78.5 cubic inches. That translates to 5.45 cups. Similarly, to get volumes for a 1.5- or 2-inch pans, multiply by 1.5 or 2 respectively. This yields volumes of 8.175 and 10.9 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 10.9 cups would be 10.9 times 0.67, or 7.3 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 1.5-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 1.5-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.
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