[tex]\displaystyle\\
\begin{cases}
R_1 = 3R_2\\
\pi R_1^2 +\pi R_2^2=12\pi ~~~\Big|~~:\pi
\end{cases} \\ \\
\begin{cases}
R_1 = 3R_2\\
R_1^2 + R_2^2=12
\end{cases} \\ \\
(3R_2)^2+ R_2^2=12 \\ \\
9R_2^2 + R_2^2=12 \\ \\
10R_2^2=12\\\\
R_2^2 = \frac{12}{10} = \frac{6}{5} \\ \\
R_2 = \boxed{\sqrt{\frac{6}{5}} } \\ \\
R_1 = \boxed{3\sqrt{\frac{6}{5}} }[/tex]
