1. **Stating the problem:** We need to find the surface area of the roof of a tower shaped like a rotational cone. 2. **Given data:** Radius of the base $r = 6$ m, height $h = 7$ m, and use $\pi = 3.14$. 3. **Formula:** The lateral surface area $A$ of a cone is given by $$A = \pi r l$$ where $l$ is the slant height. 4. **Calculate the slant height $l$:** $$l = \sqrt{r^2 + h^2} = \sqrt{6^2 + 7^2} = \sqrt{36 + 49} = \sqrt{85}$$ 5. **Approximate $l$:** $$l \approx 9.22$$ 6. **Calculate the lateral surface area:** $$A = 3.14 \times 6 \times 9.22$$ 7. **Intermediate step showing cancellation (if any):** No common factors to cancel here. 8. **Calculate:** $$A \approx 3.14 \times 6 \times 9.22 = 173.77$$ 9. **Round to the nearest whole number:** $$A \approx 174$$ **Final answer:** The surface area of the roof is approximately **174 m²**.