Which expression is the area formula for a circle in terms of its radius?

Which expression is the area formula for a circle in terms of its radius?

• A. A=2πr
• B. A=πr²
• C. A=πd²
• D. A=4πr²

Answer: (B)

The area of a circle depends on the square of its radius, with π linking the radius to the space inside. The correct expression is A = π r^2 because the area grows with r^2 and the constant π adjusts for the circle’s geometry. For example, doubling the radius makes the area four times larger, since (2r)^2 = 4r^2, which aligns with this formula. The other forms describe different things: 2πr is the circumference, the distance around the circle; πd^2 would misuse the diameter in a way that doesn’t match the standard area formula; and 4π r^2 is the surface area of a sphere, not the area of a circle.

The area of a circle depends on the square of its radius, with π linking the radius to the space inside. The correct expression is A = π r^2 because the area grows with r^2 and the constant π adjusts for the circle’s geometry. For example, doubling the radius makes the area four times larger, since (2r)^2 = 4r^2, which aligns with this formula. The other forms describe different things: 2πr is the circumference, the distance around the circle; πd^2 would misuse the diameter in a way that doesn’t match the standard area formula; and 4π r^2 is the surface area of a sphere, not the area of a circle.