1. **State the problem:** We need to approximate the volume of a sphere with radius $r = 4.8$ mm. 2. **Formula:** The volume $V$ of a sphere is given by the formula: $$V = \frac{4}{3} \pi r^3$$ where $\pi \approx 3.14$ and $r$ is the radius. 3. **Calculate the volume:** Substitute $r = 4.8$ and $\pi = 3.14$: $$V = \frac{4}{3} \times 3.14 \times (4.8)^3$$ 4. **Calculate $4.8^3$:** $$4.8^3 = 4.8 \times 4.8 \times 4.8 = 110.592$$ 5. **Substitute back:** $$V = \frac{4}{3} \times 3.14 \times 110.592$$ 6. **Multiply $3.14 \times 110.592$:** $$3.14 \times 110.592 = 347.24448$$ 7. **Multiply by $\frac{4}{3}$:** $$V = \frac{4}{3} \times 347.24448 = \cancel{\frac{4}{3}} \times 347.24448 = \frac{4 \times 347.24448}{3}$$ $$= \frac{1388.97792}{3}$$ 8. **Divide:** $$V = 462.99264$$ 9. **Round to the nearest tenth:** $$V \approx 463.0$$ **Final answer:** The volume of the sphere is approximately **463.0 mm³**.