If a circle has area A, the radius r is given by which expression?

• A. r = sqrt(A/π)
• B. r = A/π
• C. r = π/A
• D. r = A^2/π

Answer: (A)

The relationship being tested is how to get the radius from the circle’s area. A circle’s area is A = π r^2, so to solve for r you first isolate r^2 by dividing by π: r^2 = A/π. Then take the square root to get r = sqrt(A/π). This is the correct form because it correctly reverses the area formula to solve for the radius, giving a length when A is an area (length^2).

The other expressions don’t satisfy the original equation. For example, r = A/π would make r have the dimension of area, not length, and it doesn’t account for the squaring in A = π r^2. Expressions like r = π/A or r = A^2/π misplace the factors and powers entirely, leading to values that wouldn’t satisfy the circle’s area relationship in general.