If the radius of a circle doubles, what happens to its area?

If the radius of a circle doubles, what happens to its area?

• A. The area increases by a factor of 4
• B. The area doubles
• C. The area remains the same
• D. The area increases by a factor of 2

Answer: (A)

Area scales with the square of the radius. The area of a circle is A = πr^2. If the radius doubles to 2r, the new area is A' = π(2r)^2 = 4πr^2, which is four times the original area. So the area increases by a factor of 4.

Area scales with the square of the radius. The area of a circle is A = πr^2. If the radius doubles to 2r, the new area is A' = π(2r)^2 = 4πr^2, which is four times the original area. So the area increases by a factor of 4.