# You have been asked to bake the birthday cake of a little girl who is about to turn three. When looking up suggestions online on how to bake this cake

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,$$y=n(6x\pi) 2(9x\pi)=n(6x\pi) 18x\pi=n(6x\pi) n=\frac{18}{6} n=3$$