Which formula expresses the area of a circle in terms of its radius r?

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

Answer: (A)

Area grows with the square of the radius, so the correct expression is A = π r^2. The π makes the result match the actual area for circles of any size, and the r^2 shows that increasing the radius causes area to rise by a factor equal to the square of the scaling. If you substitute diameter for radius, π d becomes 2π r, which is the circle’s circumference, not its area. The form 2π r is indeed the circumference. Using just r^2 lacks the π factor, so it wouldn’t give the true area for a circle of any size.