Question: Work out the surface area of this shape in terms of $\pi$.\n\n9 cm\n5 cm\n\nShape: a cylinder with a hemisphere on top; the hemisphere height is 9 cm and the cylinder height is 5 cm, with the shared circular radius implied by the dome and cylinder.
1. **State the problem:**\nWe need to find the surface area of a shape composed of a cylinder with height $5$ cm and a hemisphere on top with height $9$ cm. Both share the same radius $r$.\n\n2. **Find the radius:**\nThe height of the hemisphere is equal to its radius, so $r = 9$ cm.\n\n3. **Surface area components:**\n- Cylinder surface area (excluding top): $2\pi r h$\n- Hemisphere surface area (curved surface only): $2\pi r^2$\n- Cylinder base area (bottom circle): $\pi r^2$\n\n4. **Calculate each part:**\n- Cylinder lateral surface area: $$2\pi \times 9 \times 5 = 90\pi$$\n- Hemisphere surface area: $$2\pi \times 9^2 = 2\pi \times 81 = 162\pi$$\n- Cylinder base area: $$\pi \times 9^2 = 81\pi$$\n\n5. **Total surface area:**\nThe top of the cylinder is covered by the hemisphere, so we do not count the cylinder's top circle.\n\n$$\text{Total surface area} = \text{Cylinder lateral} + \text{Hemisphere surface} + \text{Cylinder base}$$\n$$= 90\pi + 162\pi + 81\pi = 333\pi$$\n\n6. **Final answer:**\nThe surface area of the shape in terms of $\pi$ is $$\boxed{333\pi \text{ cm}^2}.$$