1. **State the problem:** We are given a cylinder with two circular bases, each having an area of 706.5 m², and a height of 55 m. We need to find the total surface area of the cylinder. 2. **Formula for surface area of a cylinder:** The total surface area $S$ of a cylinder is given by: $$S = 2\pi r^2 + 2\pi r h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Find the radius $r$ from the area of one circle:** The area of one circle is: $$A = \pi r^2$$ Given $A = 706.5$, we solve for $r^2$: $$r^2 = \frac{706.5}{\pi}$$ 4. **Calculate $r^2$ and $r$:** $$r^2 = \frac{706.5}{3.1416} \approx 225$$ $$r = \sqrt{225} = 15\text{ m}$$ 5. **Calculate the lateral surface area:** $$2\pi r h = 2 \times 3.1416 \times 15 \times 55$$ $$= 2 \times 3.1416 \times 825 = 2 \times 2591.55 = 5183.1\text{ m}^2$$ 6. **Calculate the total surface area:** $$S = 2 \times 706.5 + 5183.1 = 1413 + 5183.1 = 6596.1\text{ m}^2$$ **Final answer:** The surface area of the cylinder is approximately **6596.1 m²**.