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

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

• A. 2πr
• B. πr²
• C. πd
• D. 2r

Answer: (A)

Circumference is the distance around a circle and is tied to the circle’s size through the radius and the constant π. The ratio of a circle’s circumference to its diameter is π, so C = πD. Since the diameter equals twice the radius (D = 2r), substitute to get C = π(2r) = 2πr. This is the expression that uses the radius directly. It shows that you multiply the radius by 2 and by π to get the full distance around the circle. The other forms don’t fit this radius-centered view: πr^2 is the area, not the perimeter; πd uses diameter (though substituting d = 2r would still yield 2πr); 2r omits the π factor, so it’s not the full circumference.

Circumference is the distance around a circle and is tied to the circle’s size through the radius and the constant π. The ratio of a circle’s circumference to its diameter is π, so C = πD. Since the diameter equals twice the radius (D = 2r), substitute to get C = π(2r) = 2πr. This is the expression that uses the radius directly. It shows that you multiply the radius by 2 and by π to get the full distance around the circle. The other forms don’t fit this radius-centered view: πr^2 is the area, not the perimeter; πd uses diameter (though substituting d = 2r would still yield 2πr); 2r omits the π factor, so it’s not the full circumference.