Which expression represents the area of a circle with radius r?

Which expression represents the area of a circle with radius r?

• A. A = 2πr
• B. C = 2πr
• C. A = r^2π
• D. A = π r^2

Answer: (D)

The area of a circle grows with the square of the radius, so the area is proportional to r^2, with the constant of proportionality being π. The standard formula that captures this relationship is A = π r^2. This is the form most people memorize and use in calculations, and it correctly gives the area for any circle. The option with 2πr describes the circumference, not the area, so it’s not correct for area purposes. Another choice, written as r^2π, is the same quantity as π r^2 because multiplication is commutative; it represents the same area, but the conventional way to write it is π r^2, which is why that form is typically chosen.

The area of a circle grows with the square of the radius, so the area is proportional to r^2, with the constant of proportionality being π. The standard formula that captures this relationship is A = π r^2. This is the form most people memorize and use in calculations, and it correctly gives the area for any circle.

The option with 2πr describes the circumference, not the area, so it’s not correct for area purposes. Another choice, written as r^2π, is the same quantity as π r^2 because multiplication is commutative; it represents the same area, but the conventional way to write it is π r^2, which is why that form is typically chosen.