1. **State the problem:** We need to find the area of the shaded shape WXZY, which is the ring-shaped region between two sectors OWX and OYZ. 2. **Given data:** - Central angle of both sectors: $75^\circ$ - Radius of larger circle (sector OWX): $35$ cm - Radius of smaller circle (sector OYZ): $24$ cm 3. **Formula for the area of a sector:** $$\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$$ where $\theta$ is the central angle in degrees and $r$ is the radius. 4. **Calculate the area of the larger sector OWX:** $$\text{Area}_{OWX} = \frac{75}{360} \times \pi \times 35^2 = \frac{75}{360} \times \pi \times 1225$$ 5. **Calculate the area of the smaller sector OYZ:** $$\text{Area}_{OYZ} = \frac{75}{360} \times \pi \times 24^2 = \frac{75}{360} \times \pi \times 576$$ 6. **Calculate the shaded area WXZY:** $$\text{Area}_{WXZY} = \text{Area}_{OWX} - \text{Area}_{OYZ} = \frac{75}{360} \times \pi (1225 - 576)$$ 7. **Simplify inside the parentheses:** $$1225 - 576 = 649$$ 8. **Substitute and simplify:** $$\text{Area}_{WXZY} = \frac{75}{360} \times \pi \times 649$$ 9. **Simplify the fraction:** $$\frac{75}{360} = \frac{\cancel{75}}{\cancel{360}} = \frac{5}{24}$$ 10. **Final area expression:** $$\text{Area}_{WXZY} = \frac{5}{24} \times \pi \times 649 = \frac{5 \times 649}{24} \pi$$ 11. **Calculate the numerical value:** $$\frac{5 \times 649}{24} = \frac{3245}{24} \approx 135.2083$$ 12. **Multiply by $\pi$:** $$135.2083 \times 3.1416 \approx 424.6$$ **Answer:** The area of the shaded shape WXZY is approximately **424.6 cm$^2$** to 1 decimal place.