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

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

• A. Doubles
• B. Quadruples
• C. Triples
• D. Remains the same

Answer: (B)

Doubling the radius scales the area by the square of that factor. The area of a circle is 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 four. This happens because area depends on r squared, so a linear change in radius affects area quadratically. (For comparison, the circumference would only double, since it’s proportional to r, not r^2.)

Doubling the radius scales the area by the square of that factor. The area of a circle is 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 four. This happens because area depends on r squared, so a linear change in radius affects area quadratically. (For comparison, the circumference would only double, since it’s proportional to r, not r^2.)