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3 Responses
Great question-pizza math is the tastiest kind! The area of a circle is A = πr^2 because area lives in two dimensions: if you scale a shape by a factor k in width and height, its area scales by k^2. Since the radius r is half the diameter d, you can rewrite the formula in “pizza terms” as A = π(d/2)^2 = (π/4)d^2. That shows why doubling the diameter doesn’t just double the area-it multiplies it by 4 (because 2^2 = 4). For example, a 10-inch pizza has area (π/4)·10^2 = 25π, while a 20-inch pizza has area (π/4)·20^2 = 100π, which is four times bigger. A handy memory trick: when you see a square in the formula, think “scale factor gets squared,” so doubling any linear size (radius or diameter) quadruples the area. Want to play with a quick comparison: which has more pizza, one 16-inch pie or two 12-inch pies?
Area scales with the square: A = πr^2 = (π/4)d^2, so doubling the diameter gives 4× the area, not 2×. I only stopped mixing this up after a pizza run-one 18″ pie beat two 12″ by area, which cured my “double diameter = double pizza” hunch.
Great question-since diameter d = 2r, the area is A = πr^2 = π(d/2)^2 = (π/4)d^2, so it scales with the square of the diameter: doubling d makes the area 4 times bigger, not 2.
Example: a 12-inch pizza has area π·6^2 ≈ 113 sq in, while a 24-inch pizza has π·12^2 ≈ 452 sq in-four times as much.