Q: Your pizza dough recipe is for a 12″ diameter pizza. Your pizza pan is 14″ diameter. You proceed by:
a) make a thin crust pizza
b) scale the recipe by __%
I chose to scale the recipe. A twelve inch pizza pan has an area of 6 * 6 * 3.14 (π) = 113. A fourteen inch pan has an area of 7 * 7 * 3.14 = 154. The difference in area is 154 – 113 = 41. Since the existing recipe is for 12 inches, I need to scale it up by 41 / 113 * 100 = 36%.
You have a math error. You calculated circumference, not area.
If you calculate area, the original area is 113 and your new area is 154, yielding 36%. Since you only care about the proportions, you can skip multiplying by pi and just compare 36 and 49, and get the same answer.
(and if you WERE interested in circumference, you could have skipped the multiplication by pi anyway and just used 12 and 14 in your calculation and you’d have still gotten 16%).
Thanks for the correction David. I have updated the post accordingly. I’m glad I wrote my scaled recipe in the cookbook in pencil. 🙂