If the radius of a circle is doubled, the area becomes which of the following?

• A. Doubles
• B. Quadruples
• C. Increases by π
• D. Stays the same

Answer: (B)

The area of a circle grows with the square of its radius. Since the formula is A = πr^2, doubling the radius means using 2r for the radius: A' = π(2r)^2 = 4πr^2 = 4A. So the area becomes four times as large. This squaring effect explains why the area quadruples when the radius is doubled. If you scale the radius by any factor k, the area scales by k^2, so doubling gives a fourfold increase, not just a double or a small increase.