Doubling the radius of a circle increases the circumference by what factor?

Doubling the radius of a circle increases the circumference by what factor?

• A. 2x
• B. 4x
• C. 1x
• D. 3x

Answer: (A)

Doubling the radius doubles the circumference because circumference is directly proportional to the radius. With C = 2πr, if r becomes 2r, the new circumference is C' = 2π(2r) = 4πr, which is twice the original C = 2πr. So the factor is 2x. The other options would imply different relationships (quadrupling, staying the same, or tripling) that don’t match the direct proportionality between radius and circumference.

Doubling the radius doubles the circumference because circumference is directly proportional to the radius. With C = 2πr, if r becomes 2r, the new circumference is C' = 2π(2r) = 4πr, which is twice the original C = 2πr. So the factor is 2x. The other options would imply different relationships (quadrupling, staying the same, or tripling) that don’t match the direct proportionality between radius and circumference.