1. **State the problem:** We need to find the surface area of a shape made by joining a hemisphere on top of a cylinder. The hemisphere and cylinder share the same radius $r=9$ cm, and the cylinder height is $h=5$ cm. 2. **Recall formulas:** - Surface area of a sphere: $$4\pi r^2$$ - Surface area of a hemisphere (half a sphere, including the curved surface only): $$2\pi r^2$$ - Surface area of the curved side of a cylinder: $$2\pi r h$$ - Surface area of the circular base of a cylinder: $$\pi r^2$$ 3. **Important note:** The hemisphere is joined to the cylinder, so the circular base of the hemisphere and the top circle of the cylinder are not exposed surfaces. Therefore, we do not count the base of the hemisphere or the top of the cylinder separately. 4. **Calculate surface area of the shape:** - Curved surface area of hemisphere: $$2\pi r^2$$ - Curved surface area of cylinder: $$2\pi r h$$ - Base of cylinder (bottom circle): $$\pi r^2$$ (this is exposed) Total surface area $$= 2\pi r^2 + 2\pi r h + \pi r^2 = (2\pi r^2 + \pi r^2) + 2\pi r h = 3\pi r^2 + 2\pi r h$$ 5. **Substitute values:** $$r=9, \quad h=5$$ $$3\pi (9)^2 + 2\pi (9)(5) = 3\pi \times 81 + 2\pi \times 45 = 243\pi + 90\pi = 333\pi$$ 6. **Final answer:** The surface area of the shape in terms of $\pi$ is: $$\boxed{333\pi \text{ cm}^2}$$