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: 

Δa = ((π/4) * d22 - (π/4) * d12) / ((π/4) * d12)     = (d22 / d12) - 1

Helpful for the next time you want to get a wedgie in a pizza place. #math