If the circumference of a circle is tripled what happens to its radius?

Answer 1

The radius is tripled, too.

Suppose:

(1) C = 2πr

(2) C' = 2πr'

(3) C' = 3C

Then

C' = 3(2πr) = 2π(3r)

But

C' = 2πr', so 2πr' = 2π(3r)

and finally

r' = 3r.

Answer 2

The radius is directly related to the circumference of a circle by C=π 2R so it would get proportionately larger as the circumference grows.

If you start with C=π 2R where 2R=C/π then change C to C2=3C then 2R2 becomes C2/π or 3(2R)/π