Question

If the area of a circle increases by a factor of 9, by what factor does its circumference increase ?

Answer 1

a = pi r^2
A = pi R^2 = 9 a = 9 pi r^2
so
R^2 = 9 r^2
R = 3 r

c = 2 pi r
C = 2 pi R = 2 pi (3r) = 3 (2 pi r)
so
C = 3 c

Answer 2

Since A = pi*r^2
9A = pi*(3r)^2
That is, the radius grows by a factor of 3

So, since C = 2pi*r, it also grows by a factor of 3.

Just so you know, if
the linear value grows by n,
the area grows by n^2
the volume grows by n^3

Answer 3

C= 2 pi r = 2 pi (3r) = 3 ( 2 pi r )

so C = 3 c

why C = 3 c I don't understand