The circumference of a circle with radius r is

• A. 2 pi r
• B. pi r^2
• C. pi d
• D. 2 r

Answer: (A)

The key idea is that the circumference scales with the radius through the factor 2π. The distance around a circle (circumference) is C = 2πr when you know the radius r. This comes from the fact that the ratio of a circle’s circumference to its diameter is π, so C = πd. Since the diameter d equals 2r, C = π(2r) = 2πr. Because the problem gives the radius, the expression in terms of r is the most direct: 2πr. The form πd is also correct in general, but it uses diameter; substituting d = 2r returns the same result. The expression πr^2 is the area, not the circumference, and 2r lacks the π factor, so it does not represent the circle’s boundary length.