The radius of a circle increases by 20%. By what percentage does its area increase?

The area increases by 44%.

Area = pi x r^2, proportional to the square of the radius.

Radius becomes 1.2r.

New area = pi x (1.2r)^2 = 1.44 x pi x r^2.

Increase = 1.44 - 1 = 0.44 = 44%.

So the area rises 44%.