1. **Problem Statement:** Calculate the area of the shaded region swept out on a flat windscreen by a wiper. The sector has a central angle of 120° and radius lines of 4 cm and 16 cm. 2. **Formula Used:** The area of a sector of a circle is given by $$\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$$ where $\theta$ is the central angle in degrees and $r$ is the radius. 3. **Important Rules:** - The shaded region is the area between two sectors with radii 16 cm and 4 cm. - To find the shaded area, subtract the smaller sector area from the larger sector area. 4. **Calculate the area of the larger sector:** $$\text{Area}_{large} = \frac{120}{360} \times \pi \times 16^2 = \frac{1}{3} \times \pi \times 256 = \frac{256\pi}{3}$$ 5. **Calculate the area of the smaller sector:** $$\text{Area}_{small} = \frac{120}{360} \times \pi \times 4^2 = \frac{1}{3} \times \pi \times 16 = \frac{16\pi}{3}$$ 6. **Calculate the shaded area:** $$\text{Shaded Area} = \text{Area}_{large} - \text{Area}_{small} = \frac{256\pi}{3} - \frac{16\pi}{3} = \frac{240\pi}{3} = 80\pi$$ 7. **Final answer:** Using $\pi \approx \frac{22}{7}$, $$80\pi \approx 80 \times \frac{22}{7} = \frac{1760}{7} \approx 251.43 \text{ cm}^2$$ **Therefore, the area of the shaded region is approximately 251.43 cm².