1. **State the problem:** We need to find the arc length of a circle with radius $9$ m and a central angle of $25^\circ$. 2. **Formula:** The arc length $s$ of a circle is given by the formula: $$s = r \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Convert degrees to radians:** Since the angle is given in degrees, convert it to radians using: $$\theta = 25^\circ \times \frac{\pi}{180^\circ} = \frac{25\pi}{180} = \frac{5\pi}{36}$$ 4. **Calculate the arc length:** Substitute $r = 9$ m and $\theta = \frac{5\pi}{36}$ into the formula: $$s = 9 \times \frac{5\pi}{36} = \frac{45\pi}{36} = \frac{5\pi}{4}$$ 5. **Simplify and approximate:** $$s = \frac{5\pi}{4} \approx 3.93 \text{ meters}$$ **Final answer:** The arc length is approximately $3.93$ meters.