1. **State the problem:** We need to find the total surface area of a solid hemisphere with radius $8$ cm. 2. **Recall the formulas:** - Surface area of a full sphere is given by $$4\pi r^2$$. - Surface area of a hemisphere (curved surface only) is half of that: $$2\pi r^2$$. - Total surface area of a hemisphere includes the curved surface plus the flat circular base: $$2\pi r^2 + \pi r^2 = 3\pi r^2$$. 3. **Calculate the total surface area:** Given $r = 8$ cm, $$\text{Total surface area} = 3\pi (8)^2 = 3\pi \times 64 = 192\pi$$. 4. **Evaluate the numerical value:** Using $\pi \approx 3.1416$, $$192 \times 3.1416 = 603.1856$$ cm$^2$. 5. **Round to 3 significant figures:** $$603$$ cm$^2$. **Final answer:** The total surface area of the hemisphere is $603$ cm$^2$ to 3 significant figures.