If the ratio of areas of two circles is 4 : 9, then the ratio of their circumferences will be :

The area of a circle is $\pi r^2$, so $\frac{r_1^2}{r_2^2}=\frac49$ gives $\frac{r_1}{r_2}=\frac23$. Circumference $2\pi r$ varies directly with the radius, so the circumferences are also in the ratio 2 : 3. 4 : 9 repeats the ratio of the areas, which grow with the square of the radius.