1. **State the problem:** We need to find the total surface area of a hemisphere with diameter 11 meters. 2. **Recall the formula:** The surface area of a sphere is given by $$4\pi r^2$$ where $r$ is the radius. 3. **Important rule:** A hemisphere is half of a sphere, but its total surface area includes the curved surface plus the flat circular base. 4. **Calculate the radius:** Given diameter $d = 11$ m, radius is $$r = \frac{d}{2} = \frac{11}{2} = 5.5$$ m. 5. **Calculate curved surface area of hemisphere:** It is half the surface area of the sphere: $$\text{Curved area} = \frac{1}{2} \times 4\pi r^2 = 2\pi r^2$$ 6. **Calculate base area:** The base is a circle with area: $$\pi r^2$$ 7. **Total surface area of hemisphere:** Sum of curved surface and base: $$\text{Total area} = 2\pi r^2 + \pi r^2 = 3\pi r^2$$ 8. **Substitute $r=5.5$ m:** $$3\pi (5.5)^2 = 3\pi \times 30.25 = 90.75\pi$$ **Final answer:** The total surface area of the hemisphere is $$90.75\pi$$ square meters.