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

The circumference increases by 20%.

Circumference = 2 x pi x r, which is proportional to r.

Radius rises by 20%, so r becomes 1.2r.

New circumference = 2 x pi x 1.2r = 1.2 times the old.

Increase = 1.2 - 1 = 0.2 = 20%.

So the circumference rises 20%.