Friday, June 29, 2007

What Difference Does Two Inches Make? Pizza Mathematics, Part I

A few nights ago, a friend and I went out for pizza. We deliberated over whether to order a 10" or 12" (stuffed, not thin crust). We chose the larger size but didn't finish it. Knowing that my friend is a top engineer for one of the nation's premiere steel fabricators, I figured he'd enjoy the mental exercise of determining whether we made the right choice.

First, we recalled the formula we learned long ago for the area of a circle: π * r2 or "pi times the radius squared"

My friend took out his PDA, and we used 3.1416 for π. For our calculations, the value of π to ten-thousandths would be plenty, especially considering that pizza dimensions are imprecise enough to introduce a significant margin of error. This table shows how pizza diameter translates into area:

Size (inches)Area (square inches)

We discovered that the 12" pizza we ordered had 34.6 more square inches of area than the 10" pizza. Since we ate 75% of the 12" pizza (84.8 square inches), the 10" pizza would not have been big enough, assuming we would notice the difference of six square inches. That's unlikely, but at least I got a second meal out of the leftovers!

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