What is the formula for the circumference of a circle in terms of its radius?

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Multiple Choice

What is the formula for the circumference of a circle in terms of its radius?

Explanation:
Circumference is the distance around a circle, and it scales with the radius in a direct, linear way. The standard relation uses the diameter: C = πd. Since the diameter is twice the radius (d = 2r), substitute to get C = π(2r) = 2πr. This shows exactly why the formula in terms of the radius is C = 2πr. The area of a circle, in contrast, is A = πr^2, which grows with the square of the radius and is a different measurement. The other expressions mix up these concepts or mislabel them, so they don’t match the definition of circumference.

Circumference is the distance around a circle, and it scales with the radius in a direct, linear way. The standard relation uses the diameter: C = πd. Since the diameter is twice the radius (d = 2r), substitute to get C = π(2r) = 2πr. This shows exactly why the formula in terms of the radius is C = 2πr. The area of a circle, in contrast, is A = πr^2, which grows with the square of the radius and is a different measurement. The other expressions mix up these concepts or mislabel them, so they don’t match the definition of circumference.

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