If the radius of a circle is doubled, by what factor does the area increase?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If the radius of a circle is doubled, by what factor does the area increase?

Explanation:
Doubling the radius makes the area grow with the square of the radius. For a circle, A = πr^2. If the radius becomes 2r, the new area is A' = π(2r)^2 = 4πr^2 = 4A. So the area increases by a factor of 4. This quadrupling is the result of the squared relationship between area and radius. The other numerical options don’t fit because they would require different changes to the radius (for example, a linear scaling would give a factor of 2, while a larger radius increase would be needed to reach 8, etc.).

Doubling the radius makes the area grow with the square of the radius. For a circle, A = πr^2. If the radius becomes 2r, the new area is A' = π(2r)^2 = 4πr^2 = 4A. So the area increases by a factor of 4. This quadrupling is the result of the squared relationship between area and radius. The other numerical options don’t fit because they would require different changes to the radius (for example, a linear scaling would give a factor of 2, while a larger radius increase would be needed to reach 8, etc.).

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