The circumference of a circle can be expressed as

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

Answer: (D)

The key idea is that the circumference is the boundary length of the circle and it scales with the radius by the constant 2π. Using the radius, the circumference is 2πr, which directly measures how far around the circle you travel from a starting point back to the start. If you know the diameter instead, since diameter equals 2r, you can write the circumference as πd, and both forms describe the same boundary length. The other expressions refer to different quantities: πr^2 is the area of the circle, and 2r is just the diameter, not the actual distance around the edge.