1. **State the problem:** We need to find the volume of a sphere with diameter 6 units. 2. **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:** Since the diameter $d = 6$, the radius is half of the diameter: $$r = \frac{d}{2} = \frac{6}{2} = 3$$ 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. **Calculate the volume:** $$V = \frac{4}{3} \pi \times 27$$ 7. **Simplify the fraction:** $$V = \cancel{\frac{4}{3}} \pi \times \cancel{27} \times 9 = 36 \pi$$ 8. **Final answer:** The exact volume is: $$\boxed{36 \pi \text{ units}^3}$$ If you want a decimal approximation using $\pi \approx 3.14$: $$V \approx 36 \times 3.14 = 113.04 \text{ units}^3$$