This is the second in a series of posts on math in the real world.

Which piece of cake should you choose?

This is a problem that often happens at birthday parties. Should you pick a corner piece, a side piece, or one of the middle pieces?

The answer depends on whether you want to optimize for volume of cake, volume of icing, or a balance between enough icing, and enough cake. You can either view this as a volume and surface area problem (or use calculus to determine the optimal piece of cake).

It’s not hard to see that a corner piece has the most available area for icing, but it is less clear whether a middle piece or a side piece has more icing. How much of a difference does the angle in the cake make?

One obvious way to bring this problem (literally) into your classroom is to make a cake and share it with the students, which is more useful if you talk about the shapes of the pieces in advance, and get kids thinking about which piece of cake they should take, depending on their preferences. At the very least it is likely that students will never look at a birthday cake quite the same way again.