1. **State the problem:** We need to find the volume of a cone with a slant height of 16.6 yd and a base radius of 12.5 yd. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height of the cone. 3. **Find the height $h$ using the Pythagorean theorem:** The slant height $l = 16.6$ yd, radius $r = 12.5$ yd, and height $h$ form a right triangle: $$l^2 = r^2 + h^2$$ Rearranged to solve for $h$: $$h = \sqrt{l^2 - r^2}$$ 4. **Calculate $h$:** $$h = \sqrt{16.6^2 - 12.5^2} = \sqrt{275.56 - 156.25} = \sqrt{119.31} \approx 10.92$$ yd 5. **Calculate the volume $V$:** $$V = \frac{1}{3} \pi (12.5)^2 (10.92) = \frac{1}{3} \pi (156.25)(10.92)$$ $$= \frac{1}{3} \pi (1705.5) = \pi (568.5) \approx 3.1416 \times 568.5 = 1785.4$$ yd$^3$ 6. **Round to the nearest tenth:** $$\boxed{1785.4}$$ yd$^3$ is the volume of the cone.