1. **State the problem:** Calculate the volume of a cylinder with diameter $d=12$ inches and height $h=4$ inches. 2. **Formula:** The volume $V$ of a cylinder is given by $$V=\pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Find the radius:** Since diameter $d=12$ inches, $$r=\frac{d}{2}=\frac{12}{2}=6$$ inches. 4. **Substitute values:** $$V=\pi \times 6^2 \times 4=\pi \times 36 \times 4=144\pi$$ 5. **Calculate numerical value:** $$V \approx 144 \times 3.1416=452.389$$ 6. **Round to nearest tenth:** $$V \approx 452.4$$ cubic inches. **Final answer:** - In terms of $\pi$: $144\pi$ cubic inches. - Nearest tenth: $452.4$ cubic inches.