The ratio of the circumferences of two circles is 2 : 3. What is the ratio of their areas ?

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow \frac{{2\pi {R_1}}}{{2\pi {R_2}}} = \frac{2}{3} \cr & \Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{2}{3} \cr & \Rightarrow \frac{{\pi R_1^2}}{{\pi R_2^2}} = {\left( {\frac{2}{3}} \right)^2} \cr & \Rightarrow \frac{{\pi R_1^2}}{{\pi R_2^2}} = \frac{4}{9} \text{ or } 4:9 \cr} $$