1. **Problem Statement:** Find the volume of the given solid, which is a slanted cylindrical solid with a circular top and bottom, where the top diameter is 12 m, the slant height is 18 m, and the angle between the base and the slant height is 60°. 2. **Formula and Important Rules:** The volume $V$ of a cylinder is given by: $$V = \text{area of base} \times \text{height}$$ For a circular base, the area is: $$A = \pi r^2$$ where $r$ is the radius of the base. Since the cylinder is slanted, the height $h$ is the vertical height, not the slant height. We use trigonometry to find $h$ from the slant height $l$ and the angle $\theta$: $$h = l \sin(\theta)$$ 3. **Calculate the radius:** $$r = \frac{12}{2} = 6 \text{ m}$$ 4. **Calculate the height:** $$h = 18 \times \sin(60^\circ) = 18 \times \frac{\sqrt{3}}{2} = 9\sqrt{3} \text{ m}$$ 5. **Calculate the volume:** $$V = \pi r^2 h = \pi \times 6^2 \times 9\sqrt{3} = \pi \times 36 \times 9\sqrt{3} = 324\sqrt{3} \pi \text{ m}^3$$ **Final answer:** $$\boxed{324\sqrt{3} \pi \text{ cubic meters}}$$