If the radius of a circle doubles, the circumference becomes how many times as large?

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Multiple Choice

If the radius of a circle doubles, the circumference becomes how many times as large?

The key idea is that the circumference grows directly with the radius. The formula C = 2πr shows that if you change the radius, you change the circumference by the same factor, because 2π is just a constant. If the radius doubles to 2r, the new circumference becomes C' = 2π(2r) = 2(2πr) = 2C. So the circumference becomes twice as large. This rules out staying the same, tripling, or quadrupling; only a doubling of the radius leads to a doubling of the circumference.

The key idea is that the circumference grows directly with the radius. The formula C = 2πr shows that if you change the radius, you change the circumference by the same factor, because 2π is just a constant. If the radius doubles to 2r, the new circumference becomes C' = 2π(2r) = 2(2πr) = 2C. So the circumference becomes twice as large. This rules out staying the same, tripling, or quadrupling; only a doubling of the radius leads to a doubling of the circumference.

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