1. **State the problem:** Find the volume of a sphere with radius $r=3$ cm. 2. **Formula:** The volume $V$ of a sphere is given by $$V=\frac{4}{3}\pi r^3$$ 3. **Calculate volume in terms of $\pi$:** $$V=\frac{4}{3}\pi (3)^3=\frac{4}{3}\pi 27=36\pi$$ 4. **Calculate volume using $\pi \approx 3.14$:** $$V \approx 36 \times 3.14=113.04$$ 5. **Final answer:** The volume of the sphere is $36\pi$ cubic centimeters or approximately $113.0$ cubic centimeters to the nearest tenth.