If the radius of a sphere is doubled, by what factor does its surface area increase?

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Multiple Choice

If the radius of a sphere is doubled, by what factor does its surface area increase?

Explanation:
Surface area scales with the square of the radius. For a sphere, SA = 4πr^2. If the radius is doubled, the new area is 4π(2r)^2 = 16πr^2, which is four times the original area. So the surface area increases by a factor of four (four times as large). In general, doubling a linear dimension multiplies area by 4, while volume would multiply by 8.

Surface area scales with the square of the radius. For a sphere, SA = 4πr^2. If the radius is doubled, the new area is 4π(2r)^2 = 16πr^2, which is four times the original area. So the surface area increases by a factor of four (four times as large). In general, doubling a linear dimension multiplies area by 4, while volume would multiply by 8.

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