1. **State the problem:** We need to find the total surface area of a shape made by joining a hemisphere on top of a cylinder. 2. **Given:** - Radius of hemisphere and cylinder base, $r = 8$ cm - Height of cylinder, $h = 5$ cm 3. **Recall formulas:** - Surface area of a sphere: $4\pi r^2$ - Surface area of a hemisphere (half a sphere): $2\pi r^2$ - Curved surface area of a cylinder: $2\pi r h$ - Area of the circular base of the cylinder: $\pi r^2$ 4. **Important note:** The hemisphere is joined to the cylinder at the circular base, so that base is not exposed and should not be counted twice. 5. **Calculate surface area of the hemisphere:** $$\text{Hemisphere area} = 2\pi r^2 = 2\pi \times 8^2 = 2\pi \times 64 = 128\pi$$ 6. **Calculate curved surface area of the cylinder:** $$\text{Cylinder curved area} = 2\pi r h = 2\pi \times 8 \times 5 = 80\pi$$ 7. **Calculate base area of the cylinder:** $$\text{Base area} = \pi r^2 = \pi \times 8^2 = 64\pi$$ 8. **Total surface area of the shape:** Since the base of the hemisphere and the top base of the cylinder are joined, the base of the cylinder is exposed and must be included. $$\text{Total surface area} = \text{Hemisphere area} + \text{Cylinder curved area} + \text{Cylinder base area}$$ $$= 128\pi + 80\pi + 64\pi = 272\pi$$ **Final answer:** $$\boxed{272\pi \text{ cm}^2}$$