1. **State the problem:** Find the volume of a cone with base radius $r=4$ meters and height $h=9$ meters. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ This formula calculates the volume by taking one-third of the base area times the height. 3. **Substitute the given values:** $$V = \frac{1}{3} \pi (4)^2 (9)$$ 4. **Calculate the square of the radius:** $$4^2 = 16$$ 5. **Multiply inside the formula:** $$V = \frac{1}{3} \pi \times 16 \times 9$$ 6. **Multiply 16 and 9:** $$16 \times 9 = 144$$ 7. **Rewrite the volume:** $$V = \frac{1}{3} \pi \times 144$$ 8. **Simplify the fraction:** $$V = \cancel{\frac{1}{3}} \pi \times \cancel{144} 48$$ 9. **Calculate the volume using $\pi \approx 3.1416$:** $$V \approx 48 \times 3.1416 = 150.7968$$ 10. **Round to the nearest whole number:** $$V \approx 151$$ cubic meters. **Final answer:** The volume of the cone is approximately **151 cubic meters**, which corresponds to option C.