1. **State the problem:** We need to find the volume of a billiard ball which is a sphere with a diameter of 6 centimeters. 2. **Recall the formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Find the radius:** The radius $r$ is half the diameter, so $$r = \frac{6}{2} = 3 \text{ cm}$$ 4. **Substitute the radius into the volume formula:** $$V = \frac{4}{3} \pi (3)^3$$ 5. **Calculate the cube of the radius:** $$3^3 = 27$$ 6. **Substitute and simplify:** $$V = \frac{4}{3} \pi \times 27$$ 7. **Simplify the fraction:** $$V = 4 \pi \times \cancel{\frac{27}{3}} = 4 \pi \times 9 = 36 \pi$$ 8. **Calculate the numerical value using $\pi \approx 3.1416$:** $$V \approx 36 \times 3.1416 = 113.0976$$ 9. **Round to the nearest tenth:** $$V \approx 113.1 \text{ cubic centimeters}$$ **Final answer:** The volume of the billiard ball is approximately $113.1$ cubic centimeters.