1. **State the problem:** Calculate the volume of a cylinder with radius $r=4$ cm and height $h=12$ cm, giving the answer to 1 decimal place. 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. **Substitute values:** $$V = \pi \times 4^2 \times 12$$ 4. **Calculate:** $$4^2 = 16$$ $$V = \pi \times 16 \times 12 = 192\pi$$ 5. **Approximate using $\pi \approx 3.1416$:** $$V \approx 192 \times 3.1416 = 603.1856$$ 6. **Round to 1 decimal place:** $$V \approx 603.2$$ **Final answer:** The volume of the cylinder is approximately $603.2$ cm$^3$.