1. **State the problem:** Find the volume of a sphere with radius $r=2.1$ millimeters using the formula for the volume of a sphere. 2. **Formula:** The volume $V$ of a sphere is given by $$V=\frac{4}{3}\pi r^3$$ where $r$ is the radius. 3. **Substitute the values:** $$V=\frac{4}{3} \times 3.14 \times (2.1)^3$$ 4. **Calculate the cube of the radius:** $$2.1^3 = 2.1 \times 2.1 \times 2.1 = 9.261$$ 5. **Calculate the volume:** $$V=\frac{4}{3} \times 3.14 \times 9.261$$ 6. **Multiply constants:** $$\frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3} = \frac{12.56}{3}$$ 7. **Simplify the fraction:** $$\frac{12.56}{3} = 4.1866...$$ 8. **Calculate the final volume:** $$V = 4.1866... \times 9.261 = 38.78$$ 9. **Round to the nearest tenth:** $$V \approx 38.8$$ millimeters cubed. **Final answer:** The volume of the pearl is approximately **38.8** cubic millimeters.