1. **State the problem:** We need to find the volume of one hemisphere of the Earth, which is roughly spherical with a diameter of 12,800 km. 2. **Formula used:** The volume of a sphere is given by $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 3. Since a hemisphere is half of a sphere, its volume is $$V_{hemisphere} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3$$ 4. **Calculate the radius:** The diameter is 12,800 km, so the radius is $$r = \frac{12,800}{2} = 6,400 \text{ km}$$ 5. **Calculate the volume:** $$V_{hemisphere} = \frac{2}{3} \pi (6,400)^3$$ 6. Compute the cube: $$6,400^3 = 6,400 \times 6,400 \times 6,400 = 262,144,000,000$$ 7. Substitute back: $$V_{hemisphere} = \frac{2}{3} \pi \times 262,144,000,000$$ 8. Multiply constants: $$\frac{2}{3} \times 262,144,000,000 = \frac{2 \times 262,144,000,000}{3} = \frac{524,288,000,000}{3} \approx 174,762,666,667$$ 9. Multiply by $\pi$: $$V_{hemisphere} \approx 174,762,666,667 \times 3.1416 \approx 549,778,714,378 \text{ km}^3$$ 10. **Round to 3 significant figures:** $$V_{hemisphere} \approx 5.50 \times 10^{11} \text{ km}^3$$ **Final answer:** The approximate volume of each hemisphere of the Earth is $$5.50 \times 10^{11} \text{ km}^3$$.