1. **Problem Statement:** We have a ratio table for circular objects with diameters and circumferences. We need to find the missing values in the table. 2. **Formula:** The circumference $C$ of a circle is related to its diameter $d$ by the formula: $$C = \pi d$$ where $\pi \approx 3.1416$. 3. **Given Data:** - Diameter $d_1 = 42$ mm, Circumference $C_1 = 132$ mm - Diameter $d_2 = ?$, Circumference $C_2 = 198$ mm - Diameter $d_3 = 301$ mm, Circumference $C_3 = ?$ 4. **Find missing diameter $d_2$:** Since circumference is proportional to diameter, the ratio $\frac{C}{d}$ is constant. Calculate the ratio using known values: $$\frac{C_1}{d_1} = \frac{132}{42} = 3.142857... \approx \pi$$ Use this ratio to find $d_2$: $$d_2 = \frac{C_2}{\pi} = \frac{198}{3.142857} \approx 63 \text{ mm}$$ 5. **Find missing circumference $C_3$:** Use the same ratio: $$C_3 = \pi d_3 = 3.142857 \times 301 \approx 946 \text{ mm}$$ 6. **Summary of completed table:** | Diameter (mm) | 42 | 63 | 301 | | Circumference (mm) | 132 | 198 | 946 | 7. **Explanation:** The circumference and diameter of circles are directly proportional with the constant of proportionality $\pi$. We used this to find missing values by maintaining the ratio. Final answers: - Missing diameter $d_2 = 63$ mm - Missing circumference $C_3 = 946$ mm