1. **State the problem:** We are given an arc length $s = 30$ cm and a central angle $\theta = 120^\circ$ in a circle. We need to find the radius $r$ of the circle. 2. **Formula used:** The arc length $s$ of a circle is related to the radius $r$ and the central angle $\theta$ (in radians) by the formula: $$ s = r \theta $$ 3. **Convert the angle to radians:** Since $\theta$ is given in degrees, convert it to radians using: $$ \theta_{rad} = \theta_{deg} \times \frac{\pi}{180} $$ $$ \theta_{rad} = 120 \times \frac{\pi}{180} = \frac{2\pi}{3} $$ 4. **Substitute values into the arc length formula:** $$ 30 = r \times \frac{2\pi}{3} $$ 5. **Solve for $r$:** $$ r = \frac{30}{\frac{2\pi}{3}} $$ 6. **Simplify the fraction:** $$ r = 30 \times \frac{3}{2\pi} $$ $$ r = \frac{90}{2\pi} $$ $$ r = \frac{\cancel{90}}{\cancel{2}\pi} \times \frac{1}{1} = \frac{45}{\pi} $$ 7. **Final answer:** $$ r = \frac{45}{\pi} \approx 14.32 \text{ cm} $$ The radius of the circle is approximately 14.32 cm.