1. **State the problem:** Calculate the volume of a cylinder with radius $r=4$ cm and height $h=12$ cm, rounding the answer to 1 decimal place. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute the given values:** $$V = \pi \times 4^2 \times 12$$ 4. **Calculate the square of the radius:** $$4^2 = 16$$ 5. **Multiply the values:** $$V = \pi \times 16 \times 12$$ 6. **Simplify multiplication:** $$V = \pi \times 192$$ 7. **Calculate the numerical value using $\pi \approx 3.1416$:** $$V \approx 3.1416 \times 192 = 603.1856$$ 8. **Round to 1 decimal place:** $$V \approx 603.2$$ cm$^3$ **Final answer:** The volume of the cylinder is approximately $603.2$ cm$^3$.