Subjects geometry

Arc Length Ef A70Eb7

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1. **Problem:** Find the length of arc EF in a circle with radius 12 m and central angle 120°. 2. **Formula:** The length of an arc $L$ is given by $$L = r \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Convert angle to radians:** $$120^\circ = 120 \times \frac{\pi}{180} = \frac{2\pi}{3}$$ 4. **Calculate arc length:** $$L = 12 \times \frac{2\pi}{3} = \cancel{12} \times \frac{2\pi}{\cancel{3}} \times 4 = 8\pi$$ 5. **Answer:** The length of arc EF is $8\pi$ meters.