1. **State the problem:** We have a sector with a central angle of 60° and an unknown radius $r$. Its area equals the area of a circle with radius 7 cm. 2. **Formulas:** - Area of a sector: $$A_{sector} = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is the central angle in degrees. - Area of a circle: $$A_{circle} = \pi R^2$$ where $R$ is the radius of the circle. 3. **Given:** - $\theta = 60^\circ$ - $R = 7$ cm - $\pi = \frac{22}{7}$ 4. **Set the areas equal:** $$\frac{60}{360} \times \pi r^2 = \pi \times 7^2$$ 5. **Simplify the fraction:** $$\frac{60}{360} = \frac{1}{6}$$ 6. **Substitute and simplify:** $$\frac{1}{6} \times \pi r^2 = \pi \times 49$$ 7. **Divide both sides by $\pi$:** $$\cancel{\pi} \times \frac{1}{6} r^2 = \cancel{\pi} \times 49 \implies \frac{1}{6} r^2 = 49$$ 8. **Multiply both sides by 6:** $$r^2 = 49 \times 6 = 294$$ 9. **Find $r$ by taking the square root:** $$r = \sqrt{294}$$ 10. **Simplify $\sqrt{294}$:** $$294 = 49 \times 6$$ $$r = \sqrt{49 \times 6} = \sqrt{49} \times \sqrt{6} = 7 \sqrt{6}$$ **Final answer:** The radius of the sector is $$r = 7 \sqrt{6} \text{ cm}$$.