1. **State the problem:** We need to find the area of the sidewalk surrounding a circular pool with diameter 10 meters and sidewalk width 1 meter. 2. **Formula used:** Area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Calculate the radius of the pool:** Diameter = 10 m, so radius $r = \frac{10}{2} = 5$ m. 4. **Calculate the radius including the sidewalk:** Sidewalk width = 1 m, so total radius $R = 5 + 1 = 6$ m. 5. **Calculate the area of the pool plus sidewalk:** $$A_{total} = \pi R^2 = 3.14 \times 6^2 = 3.14 \times 36 = 113.04$$ square meters. 6. **Calculate the area of the pool alone:** $$A_{pool} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5$$ square meters. 7. **Calculate the area of the sidewalk:** $$A_{sidewalk} = A_{total} - A_{pool} = 113.04 - 78.5 = 34.54$$ square meters. **Final answer:** The area of the sidewalk is **34.54** square meters.