1. **State the problem:** We need to find the volume of a sphere with a diameter of 57.1 cm, rounded to the nearest tenth of a cubic centimeter. 2. **Formula:** The volume $V$ of a sphere is given by the formula: $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Find the radius:** The radius $r$ is half the diameter: $$r = \frac{57.1}{2} = 28.55 \text{ cm}$$ 4. **Calculate the volume:** Substitute $r = 28.55$ into the volume formula: $$V = \frac{4}{3} \pi (28.55)^3$$ 5. **Intermediate calculation:** Calculate $28.55^3$: $$28.55^3 = 28.55 \times 28.55 \times 28.55 = 23288.79$$ 6. **Substitute and simplify:** $$V = \frac{4}{3} \pi \times 23288.79$$ 7. **Calculate the fraction:** $$\frac{4}{3} \times 23288.79 = \cancel{\frac{4}{3}} \times 23288.79 = 4 \times \frac{23288.79}{3} = 4 \times 7762.93 = 31051.72$$ 8. **Multiply by $\pi$:** $$V = 31051.72 \times \pi \approx 31051.72 \times 3.1416 = 97544.3$$ 9. **Round the result:** The volume rounded to the nearest tenth is: $$97544.3 \text{ cm}^3$$ **Final answer:** The volume of the sphere is approximately $97544.3$ cubic centimeters.