1. **State the problem:** We need to find the surface area of a right circular cylinder with height $h=19$ in and diameter $d=13$ in, using $\pi=3.14$. 2. **Recall the formula for surface area of a cylinder:** $$\text{Surface Area} = 2\pi r^2 + 2\pi r h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radius:** $$r = \frac{d}{2} = \frac{13}{2} = 6.5 \text{ in}$$ 4. **Calculate the lateral surface area:** $$2\pi r h = 2 \times 3.14 \times 6.5 \times 19$$ $$= 2 \times 3.14 \times 123.5 = 2 \times 387.79 = 775.58 \text{ in}^2$$ 5. **Calculate the area of the two bases:** $$2\pi r^2 = 2 \times 3.14 \times (6.5)^2 = 2 \times 3.14 \times 42.25 = 2 \times 132.57 = 265.14 \text{ in}^2$$ 6. **Calculate total surface area:** $$\text{Surface Area} = 775.58 + 265.14 = 1040.72 \text{ in}^2$$ 7. **Compare with given answer:** The given surface area is about 2612.48 in$^2$, which is much larger than our calculation. 8. **Likely error:** The given value 775.6 in$^2$ matches the lateral surface area calculation, so the error was likely omitting the area of the two circular bases and reporting only the lateral surface area as the total surface area. **Final answer:** The total surface area is approximately $1040.72$ in$^2$. The likely error was using only the lateral surface area and not adding the areas of the two bases.