Assuming the 9 by 13 inch pan has sides about 2 inches high, it can hold a volume of 14 to 15 cups. Since there are 4 cups in 1 quart, the pan holds between 3 1/2 and 3 3/4 quarts.
A 9 by 13 by 2-inch cake pan can be substituted with two 9-inch round cake pans or two 8-inch square cake pans; these containers hold roughly the same volume. In baking, the amount of bake time changes when the size of the pan changes. In an oven heated to 350 degrees Fahrenheit, a cake in a 9 by 13 by 2-inch baking pan will take about 30 to 35 minutes to cook.