1. **Problem Statement:** Calculate the volume of a cone with height $25$ m and radius $11.5$ m. 2. **Formula:** The volume $V$ of a cone is given by $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute values:** $$V = \frac{1}{3} \pi (11.5)^2 (25)$$ 4. **Calculate radius squared:** $$11.5^2 = 132.25$$ 5. **Multiply inside the parentheses:** $$132.25 \times 25 = 3306.25$$ 6. **Apply the fraction:** $$V = \frac{1}{3} \pi \times 3306.25$$ 7. **Simplify the fraction:** $$V = \pi \times \cancel{\frac{1}{3}} \times 3306.25$$ 8. **Calculate volume:** $$V = \pi \times 1102.0833... \approx 3462.39$$ 9. **Final answer:** $$\boxed{3462.39 \text{ cubic meters}}$$ This is the volume of the cone with the given dimensions.