1. **State the problem:** Find the volume of a sphere with radius $r = 8$ cm. 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:** Using $\pi = 3.14$ and $r = 8$ cm, $$V = \frac{4}{3} \times 3.14 \times 8^3$$ 4. **Calculate the cube of the radius:** $$8^3 = 8 \times 8 \times 8 = 512$$ 5. **Substitute back:** $$V = \frac{4}{3} \times 3.14 \times 512$$ 6. **Multiply numerator terms:** $$4 \times 3.14 \times 512 = 6425.92$$ 7. **Divide by 3:** $$V = \frac{6425.92}{3}$$ 8. **Show cancellation:** $$V = \frac{\cancel{6425.92}}{\cancel{3}} = 2141.9733...$$ 9. **Round to the nearest tenth:** $$V \approx 2142.0 \text{ cm}^3$$ **Final answer:** The volume of the sphere is approximately $2142.0$ cm$^3$.