1. **Stating the problem:** Calculate the volume of a cylinder with diameter $d=8$ cm. 2. **Formula used:** 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 (or length) of the cylinder. 3. **Given information:** Diameter $d = 8$ cm, so radius $r = \frac{d}{2} = 4$ cm. Height $h = 8$ cm. 4. **Calculate volume in terms of $\pi$:** $$V = \pi \times 4^2 \times 8 = \pi \times 16 \times 8 = 128\pi$$ 5. **Calculate numerical value:** Using $\pi \approx 3.1416$, $$V \approx 128 \times 3.1416 = 402.123$$ Rounded to the nearest tenth: $$V \approx 402.1$$ **Final answer:** Volume $V = 128\pi$ cm$^3$ or approximately $402.1$ cm$^3$.