1. **State the problem:** We need to find the volume of a cone with a height of 25 meters and a radius of 11.5 meters. 2. **Formula for the volume of a cone:** The volume $V$ of a cone is given by the formula: $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the given values:** $$V = \frac{1}{3} \pi (11.5)^2 (25)$$ 4. **Calculate the square of the radius:** $$11.5^2 = 132.25$$ 5. **Substitute and simplify:** $$V = \frac{1}{3} \pi (132.25)(25)$$ 6. **Multiply inside the parentheses:** $$132.25 \times 25 = 3306.25$$ 7. **Volume expression:** $$V = \frac{1}{3} \pi (3306.25)$$ 8. **Divide by 3:** $$V = \pi \times \cancel{\frac{3306.25}{3}} = \pi \times 1102.0833...$$ 9. **Multiply by $\pi \approx 3.1416$:** $$V \approx 3.1416 \times 1102.0833 = 3462.39$$ 10. **Final answer:** The volume of the cone is approximately **3462.39 cubic meters**.