If the radius of a circle is increased by a factor of x, then the area is increased by what factor?
If the radius of a circle is increased by a factor of x, then the area of the circle is increased by a factor of x^2.
This can be shown using the formula for the area of a circle, which is A = πr^2.
If the radius is increased by a factor of x, the new radius will be rx. Therefore, the new area will be A' = π(rx)^2 = πr^2x^2 = x^2(πr^2) = x^2A.
So, the area is increased by a factor of x^2.