1. **State the problem:** Find the volume of a sphere with a diameter of 8 cm. 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, so: $$r = \frac{8}{2} = 4 \text{ cm}$$ 4. **Calculate the volume:** Substitute $r = 4$ cm into the volume formula: $$V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi (64) = \frac{256}{3} \pi$$ 5. **Simplify and approximate:** $$V \approx \frac{256}{3} \times 3.1416 \approx 268.08 \text{ cm}^3$$ **Final answer:** The volume of the sphere is approximately $268.08$ cubic centimeters.