1. **State the problem:** Find the volume of the oblique cylinder with given dimensions: base radius $r=5$, height $h=10$, and slant angle $40^\circ$. 2. **Formula for volume of a cylinder:** The volume $V$ of a right cylinder is given by $$V = \pi r^2 h$$ For an oblique cylinder, the volume is the same as a right cylinder with the same base and height because volume depends on the perpendicular height. 3. **Identify the perpendicular height:** Given the slant height $h=10$ and angle $40^\circ$, the perpendicular height $h_\perp$ is $$h_\perp = h \times \cos(40^\circ)$$ 4. **Calculate the perpendicular height:** $$h_\perp = 10 \times \cos(40^\circ) \approx 10 \times 0.7660 = 7.66$$ 5. **Calculate the volume:** $$V = \pi \times 5^2 \times 7.66 = \pi \times 25 \times 7.66 = 191.5\pi$$ 6. **Final answer:** $$V \approx 191.5 \times 3.1416 = 601.3$$ cubic units. **Answer:** The volume of the oblique cylinder is approximately $601.3$ cubic units.