1. **State the problem:** Find the volume of a cone with radius $r=4$ m and height $h=15$ m, expressing the answer in terms of $\pi$. 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:** $$V = \frac{1}{3} \pi (4)^2 (15)$$ 4. **Calculate the square of the radius:** $$4^2 = 16$$ 5. **Substitute and simplify:** $$V = \frac{1}{3} \pi \times 16 \times 15$$ 6. **Multiply 16 and 15:** $$16 \times 15 = 240$$ 7. **Substitute back:** $$V = \frac{1}{3} \pi \times 240$$ 8. **Simplify the fraction:** $$V = \pi \times \frac{240}{3} = \pi \times \cancel{\frac{240}{3}} = 80\pi$$ 9. **Final answer:** The volume of the cone is $$\boxed{80\pi \text{ cubic meters}}$$