What is the formula for the area of a circle in terms of its radius r?

• A. A = πr
• B. A = πr²
• C. A = πd
• D. A = 2πr

Answer: (B)

Area scales with the square of the radius. The amount of surface inside a circle grows quadratically as you increase how far points extend from the center, so the formula must involve r squared. The exact relationship that fits this scaling is A = πr^2, with π appearing as the constant of proportionality.

This matches intuition: if you double the radius, the area becomes four times larger. Forms like πr or πd would give a linear measure, not an area, and 2πr corresponds to the circle’s circumference, not its area. If you expressed area in terms of diameter, you’d get A = πd^2/4. Therefore, the correct expression is A = πr^2.