The question you opened
One 16 inch pizza or two 10 inch ones
The counter offers one 16 inch pizza or two 10 inch pizzas for the same money.
Which order gives you more pizza?
The 16 inch one
Area grows with the square of the width. One 16 inch circle is 201 square inches, and two 10 inch circles together come to 157.
A pizza is priced by its diameter and eaten by its area, and those two numbers do not move together. Area is pi times the radius squared. The 16 inch pizza has a radius of 8, so its area is pi times 64, about 201 square inches. Each 10 inch pizza has a radius of 5, so its area is pi times 25, about 78.5 square inches, and two of them come to about 157.
The single large pizza wins by roughly 28 percent. The shortcut skips pi entirely. Compare the diameters as a ratio and square it. One 16 against one 10 is a ratio of 1.6, and 1.6 squared is 2.56, so the large pizza is two and a half times one small one. Two small ones only reach 2, which is short of 2.56.
Any time shapes are similar, the ratio of areas is the square of the ratio of lengths, and the ratio of volumes is the cube. This is why large pizzas are almost always the better price per square inch, and why the gap widens as the sizes spread apart. An 18 inch pizza beats two 12 inch pizzas by a similar margin.
Going the other way, a 12 inch is only about 44 percent of an 18 inch, so ordering two smalls to feed the same table rarely works out. The same squaring runs through daily life. A television advertised as 65 inches has a screen about 44 percent larger than a 55 inch, because both numbers are diagonals. A 20 inch pipe carries roughly four times the water of a 10 inch pipe.
Doubling the radius of a coffee cup quadruples what it holds, which is why a small increase in cup size raises the price so much. The habit is to notice when a single number describes a length while the thing being bought is an area or a volume, and to square or cube the ratio before comparing prices.
Technique: Square the ratio