I once taught private lessons in math on calculating the area of a circle and I wanted to show the students how much cheaper per area a larger pizza is. So we of course got the diameters of pizzas from their favorite restaurant and started calculating. Then we found out that the normal sized pizza was actually the cheapest per area. It wasn‘t quite what we expected, but a very good math lesson for the attendees nonetheless: The owner lost money, because they were bad at maths.
Did you take into account that the crust takes away area from the "filling"? Because me and my husband also once did the math (not sure if we were frugal, bored or broke) and it all came down on whether you eat/enjoy the crust or not
ok but that picture is clearly one 18" pizza vs two 18" pizzas that have been hit by a shrink ray, meaning the two on the right have twice as much nutrition as the one on the left.
A pizza is larger than two of another just before it hits 1.5 times the radius (sqrt 2 times, to be exact, about 1.41). So if the radius is 1.5 times bigger, like in the OP, you always know it's more than twice the area.
Domino's is hardly considered pizza by most but it's $7 for a 12in. A 18in is $20. That's almost 3 pizzas. And the 12in has 2 toppings. The 18in has 0 toppings.
Dominos actually got better. It's not amazing but they took it on the chin a few years back and were like, "our pizza sucks. We need to do better" and they actually improved it quite a bit.
The math only really works for 18+ inch pizzas though. The pizza places around me don't even offer 18 inch pizzas. 14" large or 16" XL are the highest they go. In that case at most places near me, two twelves is often cheaper per square inch and does have more area than one 14" or 16". Especially since Domino's usually has coupons for two 12s that make it significantly cheaper than 1 L or XL.
Factor in the crust ratio of those though. We're talking 1.5 inch of crust, so 16" vs 12" is actually more like comparing 13" to 9" of pizza with cheese and topping. 132 v 64 square inches. You're getting 70 squares inches of crust on that 16", and 49 square inches of crust on the 12 inch. So more total food on 2 12s, but a lot more crust than one 16.
given a choice, i usually go with larger pizzas for crispy thin crust (also cut those in squares); and smaller ones for 'deep dish' or pan, where there isn't really an outside 'crust'.
I found myself making a similar calculation recently - I have a project car, and when I dragged it out of a field and hacked the vegetation out of the engine compartment, there was a 40mm motorcycle carburetor mounted to an adapter mounted to the intake. The carburetor even had a Harley-Davidson logo embossed in it.
I wanted to put a two-barrel Weber carb on it, which had a 36 mm and a 32 mm throttle plate. The 40 mm motorcycle carb had an area of 1256 mm2, while the combined area for the Weber was more like 1820 mm2.