What is the formula for the cross-sectional area of a circle given the radius r?

• A. A = π × r²
• B. A = 2 × π × r
• C. A = π × D
• D. A = r × D

Answer: (A)

For a circle, the amount of space inside it—its cross-sectional area—depends on how far the edge is from the center, the radius. The area grows with the square of the radius, and the constant of proportionality is π, so the area is A = π r².

Why this form makes sense: if you double the radius, the circle’s area becomes four times as large, since r² quadruples, while π stays the same. This contrasts with other common formulas: 2πr is the circumference, not area; π times the diameter is also a form related to the circumference; and r times the diameter doesn’t give the standard area units.

Thus, the best expression for the cross-sectional area with radius r is A = π r².