1. **State the problem:** Find the surface area of a cylinder with diameter 14.4 inches and height 15.6 inches. 2. **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:** The diameter is 14.4 inches, so the radius is half of that: $$r = \frac{14.4}{2} = 7.2 \text{ inches}$$ 4. **Substitute values into the formula:** $$\text{Surface Area} = 2 \times 3.14 \times (7.2)^2 + 2 \times 3.14 \times 7.2 \times 15.6$$ 5. **Calculate each part:** $$2 \times 3.14 \times (7.2)^2 = 2 \times 3.14 \times 51.84 = 325.7088$$ $$2 \times 3.14 \times 7.2 \times 15.6 = 2 \times 3.14 \times 112.32 = 704.6784$$ 6. **Add the two parts:** $$325.7088 + 704.6784 = 1030.3872$$ 7. **Round to the nearest hundredth:** $$\boxed{1030.39 \text{ square inches}}$$ This is the total surface area of the cylinder.