1. **State the problem:** We need to find the surface area of a hemispherical dome with radius $r = 6$ cm. 2. **Formula for surface area of a hemisphere:** The surface area of a hemisphere (half of a sphere) is given by $$\text{Surface Area} = 2\pi r^2$$ where $r$ is the radius of the hemisphere. 3. **Calculate the surface area:** Substitute $r = 6$ cm into the formula: $$\text{Surface Area} = 2\pi (6)^2 = 2\pi \times 36 = 72\pi$$ 4. **Interpretation:** The surface area of the hemispherical dome is $72\pi$ square centimeters. 5. **Approximate value:** Using $\pi \approx 3.1416$, $$72\pi \approx 72 \times 3.1416 = 226.195$$ **Final answer:** The surface area of the hemispherical dome is $72\pi$ cm$^2$ or approximately 226.2 cm$^2$.