1. **State the problem:** We need to find the area of a sector of a circle with radius $9$ cm and central angle $140^\circ$. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$ A = \frac{\theta}{360} \times \pi r^2 $$ 3. **Substitute the known values:** Here, $r = 9$ cm and $\theta = 140^\circ$. $$ A = \frac{140}{360} \times \pi \times 9^2 $$ 4. **Calculate the area:** $$ A = \frac{140}{360} \times \pi \times 81 = \frac{140}{360} \times 3.1416 \times 81 $$ 5. **Simplify step-by-step:** $$ \frac{140}{360} = \frac{7}{18} $$ $$ A = \frac{7}{18} \times 3.1416 \times 81 $$ $$ A = \frac{7}{18} \times 254.4696 $$ $$ A = 7 \times 14.1372 = 98.9604 $$ 6. **Round to 1 decimal place:** $$ A \approx 99.0 \text{ cm}^2 $$ **Final answer:** The area of the sector is approximately $99.0$ cm$^2$.