|Planet Money wrote about the economics of pizza size, but I feel like they left out the actual math. It's not complicated, but basically since
area = π*radius2 = (π/4)*diameter2, the area changes with the square of the diameter. So for an 8-inch pizza, the area is 50 square inches, while the area of a 12-inch pizza is 113 square inches. A 50% increase in diameter equates to a 125% increase in area. That's the power of exponents.
Simplifying the formula, you can write that the change in area is related to the change in diameter as follows:
Helpful for the next time you want to get a wedgie in a pizza place. #math
Δa = ((π/4)*d22 - (π/4)*d12)/((π/4)*d12) = (d22/d12) - 1