Volume of 9-inch cake pan: Let the height of the 9-inch cake pan =x. The formula to calculate the volume of a cake pan, \(V= \pi r^2h\), where h is the height of the pan. Therefore, the volume of the 9-inch cake pan, \(V= 9x\pi\). This implies the 9 inch cake pan can hold 9xπ litres of cake batter. Volume of 6-inch cake pan: Assume that all cake pans are the same height. Then the height of the 6-inch cake pan =x. The volume of the 6-inch cake pan, \(V= 6x\pi\). This implies the 6 inch cake pan can hold 6xπ litres of cake batter. Given that the recipe fills two 9 inch cake pans. Say, the recipe yields y litres of cake batter. Then, \(y=2(9x\pi)\)To find the number of cake pans to be bought: Let the number of cake pans to be bought =n. Then, we need to find n such that,\(y=n(6x\pi) 2(9x\pi)=n(6x\pi) 18x\pi=n(6x\pi) n=\frac{18}{6} n=3\)