1. **Problem:** On a circle of radius 10 m, find the length of an arc subtending a central angle of (a) $\frac{4\pi}{5}$ radians, (b) 110°. 2. **Formula:** Arc length $s$ is given by $$s = r \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Important:** If the angle is in degrees, convert to radians first using $$\theta_{rad} = \theta_{deg} \times \frac{\pi}{180}$$ 4. **Part (a):** Given $r=10$ m and $\theta = \frac{4\pi}{5}$ radians, $$s = 10 \times \frac{4\pi}{5} = \frac{40\pi}{5} = 8\pi$$ 5. **Part (b):** Given $r=10$ m and $\theta = 110^\circ$, Convert to radians: $$\theta = 110 \times \frac{\pi}{180} = \frac{110\pi}{180} = \frac{11\pi}{18}$$ Calculate arc length: $$s = 10 \times \frac{11\pi}{18} = \frac{110\pi}{18} = \frac{55\pi}{9}$$ 6. **Final answers:** - (a) $8\pi$ meters - (b) $\frac{55\pi}{9}$ meters These represent the lengths of the arcs subtending the given angles on the circle of radius 10 m.