Geometry 101: or How I Pissed Off The Waitress at a Pizza Place

So I was visiting the newly opened branch of the local upscale chain, Spin! Neapolitan Pizza. I am very picky about pizza restaurants. This stems from the undeniable truth that the best pizza in the world costs about 2-3 bucks a slice on any given corner in New York. The attempts to recreate authentic Italian pizza or to invent novel gourmet flavor combos, albeit tasty, are usually not superior experiences to the average corner NYC slice. If I am going to pay 10 or 20 dollars for something fancy, it should follow the axiom, you get what you pay for. That's why when you walk into a crappy pizza by the slice joint where you have to eat your pizza standing, you are paying for flavor, not leather booths. At Spin! what I didn't get was the truth.
This is where the math gets really hectic. The waitress told our group, two people could split a 12" pizza, but that it would probably not fill us up and that we should probably order side salads. Also, she said it was financially favorable to each get 6" individual pizza and salad combos rather than split 12" pizzas and buy the salad on the side. She said, you get the same amount of pizza and it costs a dollar less per person. She said a mouthful.

I told her, "I'm not good at math, but I'm pretty sure if you double the diameter of a circle, the area increases by 4 times, not 2."
Here comes the deer in the headlights, "6 inches is half of 12 inches."
"I might have to double check at home with cardboard cutouts, but that's unfortunately too simple to be true."

My friends are dying of embarrassment. We settle on the 6" pizza salad combos and I stew while we wait at our plush leather booth for our 8 dollar 28 sq inch pizzas. Had we ordered the 12" we could have split 113 sq inches giving each of us roughly 56 sq inches of pizza a piece. Granted, a side salad was 4.50 and a 12" pizza was 10.50. The combo we got was 8.95 a person. For two people we were paying about 18 bucks. If we went my way and bought the 12" pizza it would have cost $9 for two side salads plus 10.50 for the pizza or $19.50. A full 150 pennies, or 75 cents per person to double are pizza consumption. That said, do I need that much pizza, no, but everyone was starving at the end.

19.50 versus 18
113 sq inches vs 56 sq inches of pizza
2 salads vs 2 salads

But remember, if we had gotten twice as much pizza, we probably could have skipped the salad and still been more full. So the more realistic comparison is

10.50 versus 18
113 sq inches vs 56 sq inches of pizza
0 salads vs 2 salads

I'm pretty sure that 10.50 for more pizza is > 18 bucks for half as much pizza. Nice effort on the sales part, but at least know the hustle you are trying to run. Financially favorable? Please. I am never going back to Spin! Pizza. Next time if I want to get ripped off I'll go to dennys.

Note
Area of a circle equals 3.14 X radius X radius