1. **Problem statement:** The ratio of the radii of two circles is given as 8 : 9. We need to find the ratio of their circumferences and the ratio of their areas. 2. **Formulas used:** - Circumference of a circle: $$C = 2\pi r$$ - Area of a circle: $$A = \pi r^2$$ 3. **Ratio of circumferences:** Given the radii ratio $$r_1 : r_2 = 8 : 9$$ The ratio of circumferences is: $$\frac{C_1}{C_2} = \frac{2\pi r_1}{2\pi r_2} = \frac{r_1}{r_2} = \frac{8}{9}$$ 4. **Ratio of areas:** Using the area formula: $$\frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2^2} = \frac{r_1^2}{r_2^2} = \frac{8^2}{9^2} = \frac{64}{81}$$ 5. **Final answers:** - Ratio of circumferences = 8 : 9 - Ratio of areas = 64 : 81 These ratios show that circumference ratio is the same as the radius ratio, while the area ratio is the square of the radius ratio.