How does the area of a circle change when the radius doubles?

How does the area of a circle change when the radius doubles?

• A. It doubles
• B. It remains the same
• C. It quadruples
• D. It halves

Answer: (C)

Doubling the radius makes the area grow by a factor of four because the area of a circle is proportional to the square of the radius: A = πr^2. If r becomes 2r, the new area is A' = π(2r)^2 = 4πr^2, which is four times the original. So the area quadruples. This follows the general rule: scaling a linear dimension by k scales area by k^2. Doubling the radius does not simply double the area and it certainly isn’t unchanged.

Doubling the radius makes the area grow by a factor of four because the area of a circle is proportional to the square of the radius: A = πr^2. If r becomes 2r, the new area is A' = π(2r)^2 = 4πr^2, which is four times the original. So the area quadruples. This follows the general rule: scaling a linear dimension by k scales area by k^2. Doubling the radius does not simply double the area and it certainly isn’t unchanged.