1. **State the problem:** We have a sector AOB of a circle with an arc length of $8\pi$ cm. When folded, the sector forms a cone. We need to find the radius of the base of this cone. 2. **Recall formulas:** - Arc length of a sector: $L = r \theta$ where $r$ is the radius of the original circle and $\theta$ is the central angle in radians. - When the sector is folded into a cone, the arc length $L$ becomes the circumference of the cone's base: $C = 2\pi R$ where $R$ is the radius of the cone's base. 3. **Given:** - Arc length $L = 8\pi$ 4. **Relate arc length to cone base circumference:** Since the arc length forms the base circumference, $$8\pi = 2\pi R$$ 5. **Solve for $R$:** Divide both sides by $2\pi$: $$\cancel{8\pi} \div \cancel{2\pi} = R$$ $$4 = R$$ 6. **Answer:** The radius of the base of the cone is $4$ cm.