1. **State the problem:** We have a large circle with radius $15$ cm and a smaller circle with radius $8$ cm cut out from its center. We need to find the area of the resulting ring-shaped figure (annulus). 2. **Formula used:** The area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Calculate the area of the large circle:** $$A_{large} = \pi \times 15^2 = \pi \times 225 = 225\pi$$ 4. **Calculate the area of the smaller circle (hole):** $$A_{small} = \pi \times 8^2 = \pi \times 64 = 64\pi$$ 5. **Calculate the area of the annulus (ring):** $$A_{ring} = A_{large} - A_{small} = 225\pi - 64\pi = (225 - 64)\pi = 161\pi$$ 6. **Evaluate the numerical value:** $$A_{ring} \approx 161 \times 3.1416 = 505.5$$ 7. **Final answer:** The area of the shape is approximately **505.5 cm²** to 1 decimal place.