1. **State the problem:** We need to find the volume of a cylinder with diameter $6$ cm and height $50$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radius:** The radius $r$ is half the diameter: $$r = \frac{6}{2} = 3 \text{ cm}$$ 4. **Substitute values into the formula:** $$V = \pi \times 3^2 \times 50$$ 5. **Simplify:** $$V = \pi \times 9 \times 50 = 450\pi$$ 6. **Final answer:** $$V = 450\pi \text{ cm}^3 \approx 1413.72 \text{ cm}^3$$ The volume of the cylinder is approximately $1413.72$ cubic centimeters.