1. **State the problem:** Calculate the surface area of a cone with height $12$ feet, slant height $15$ feet, and radius $9$ feet. 2. **Formula used:** The total surface area $A$ of a cone is given by: $$A = \pi r^2 + \pi r l$$ where $r$ is the radius and $l$ is the slant height. 3. **Calculate the base area:** $$\pi r^2 = \pi \times 9^2 = 81\pi$$ 4. **Calculate the lateral surface area:** $$\pi r l = \pi \times 9 \times 15 = 135\pi$$ 5. **Calculate total surface area:** $$A = 81\pi + 135\pi = 216\pi$$ 6. **Evaluate the numerical value:** Using $\pi \approx 3.1416$, $$216\pi \approx 216 \times 3.1416 = 678.24$$ 7. **Final answer:** The total surface area of the cone is approximately **678.24 feet squared**.