1. **State the problem:** Find the surface area of a right circular cone with height $19$ cm and base radius $3$ cm, using $\pi = 3.14$. 2. **Formula for surface area of a cone:** $$\text{Surface Area} = \pi r^2 + \pi r l$$ where $r$ is the radius of the base and $l$ is the slant height. 3. **Find the slant height $l$:** Use the Pythagorean theorem since the cone is right circular: $$l = \sqrt{r^2 + h^2} = \sqrt{3^2 + 19^2} = \sqrt{9 + 361} = \sqrt{370}$$ 4. **Calculate $l$:** $$l \approx 19.235$$ 5. **Calculate the surface area:** $$\text{Surface Area} = 3.14 \times 3^2 + 3.14 \times 3 \times 19.235$$ $$= 3.14 \times 9 + 3.14 \times 57.705$$ $$= 28.26 + 181.07 = 209.33$$ 6. **Round to the nearest whole number:** $$\boxed{209} \text{ cm}^2$$ The surface area of the cone is about 209 cm².