The circumference of a circle of radius r is given by which formula?

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Multiple Choice

The circumference of a circle of radius r is given by which formula?

The circumference depends on the circle’s size through the radius, and the link uses diameter: C = πd. Since the diameter is twice the radius (d = 2r), substitute to get C = π(2r) = 2πr. This shows why the circumference grows in direct proportion to the radius with the factor 2π. Why the other forms don’t fit: πr would be missing the factor of 2, so it would be half the actual circumference. πr^2 is the area, not the distance around the circle. 4πr doesn’t come from the standard relationship between radius and circumference.

The circumference depends on the circle’s size through the radius, and the link uses diameter: C = πd. Since the diameter is twice the radius (d = 2r), substitute to get C = π(2r) = 2πr. This shows why the circumference grows in direct proportion to the radius with the factor 2π.

Why the other forms don’t fit: πr would be missing the factor of 2, so it would be half the actual circumference. πr^2 is the area, not the distance around the circle. 4πr doesn’t come from the standard relationship between radius and circumference.

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