we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter of the circle
In this problem we have
the circumference of the circle [tex]1[/tex] is
[tex]C=12\pi\ units[/tex] ------> equation A
the circumference of the circle [tex]2[/tex] is
[tex]C'=\pi D'\ units[/tex] ------> equation B
and the ratio of the circumference of the circle [tex]1[/tex] to the circumference of the circle [tex]2[/tex] is
[tex]\frac{C}{C'}=3[/tex] ------> equation C
Substitute the equation A and equation B in the equation C
[tex]\frac{12\pi}{\pi D'}=3[/tex]
[tex]D'=\frac{12}{3}=4\ units[/tex]
Find the radius r'
[tex]r'=D'/2[/tex]
[tex]r'=4/2=2\ units[/tex]
therefore
the answer is the option A
[tex]2\ units[/tex]
