Math & Statistics · 圆面积（Circle Area） · Updated 2026-10-25
What Is Circle Area?
Definition
Circle area A=πr²=π(d/2)² and circumference C=2πr=πd. The squared relation is the key intuition: scale radius by k and area scales by k² — a 12-inch pizza has 4× the area of a 6-inch at far less than 4× the price. Sector area = πr²×(angle/360°); annulus = π(R²−r²). π = 3.14159…; engineering use of 3.1416 errs under 0.0002.
Formula
A = πr²; C = 2πr; sector = πr² × θ/360°
Worked Example
A 9-inch pizza costs 68 and a 12-inch 98: area ratio (12/9)² = 1.78, so the 12-inch equals a 55-yuan 9-inch per unit area — 19% cheaper.
Common Misconception
"Double the diameter, double the area" — it quadruples. And "3.14 is enough" — for a 100 m radius tank the error is 0.0016×100² ≈ 16 m²; use 3.1416 or full calculator precision.
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