Answer: The correct option is (B) \(\dfrac{49a^2}{81b^2}.\)
Step-by-step explanation: Given that the scale factor between two circles is \(\dfrac{7a}{9b}\).
We are to find the ratio of the areas of the two circles.
Let r and R be the radii of the two circles and A and B be the corresponding areas.
We know that the scale factor is the ratio of the radii of the two circles.
So, we have
\(\dfrac{r}{R}=\dfrac{7a}{9b}\\\\\\\Rightarrow \dfrac{r^2}{R^2}=\dfrac{49a^2}{81b^2}\\\\\\\Rightarrow \dfrac{\pi r^2}{\pi R^2}=\dfrac{49a^2}{81b^2}\\\\\\\Rightarrow \dfrac{A}{B}=\dfrac{49a^2}{81b^2}.\)
Thus, the required ratio of the areas of the two circles is \(\dfrac{49a^2}{81b^2}.\)
Option (B) is CORRECT.
