1. **Problem statement:** A sector with a central angle of 108 degrees is cut from a circle of radius 20 cm. This sector is then folded to form a cone. We need to find the base radius of the cone. 2. **Formula and concepts:** When the sector is folded into a cone, the arc length of the sector becomes the circumference of the cone's base. - The circumference of the cone's base is $C = 2\pi r$, where $r$ is the base radius. - The arc length of the sector is $L = \frac{\theta}{360} \times 2\pi R$, where $\theta$ is the sector angle and $R$ is the original circle radius. 3. **Calculate the arc length of the sector:** $$L = \frac{108}{360} \times 2\pi \times 20 = \frac{3}{10} \times 2\pi \times 20 = 12\pi$$ 4. **Set the arc length equal to the circumference of the cone base:** $$2\pi r = 12\pi$$ 5. **Solve for $r$:** $$r = \frac{12\pi}{2\pi} = 6$$ 6. **Answer:** The base radius of the cone is $6$ cm.