1. **Problem:** Find the volume of a cone with radius 4 m and height 10 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. **Step-by-step solution:** - Substitute $r=4$ and $h=10$ into the formula: $$V = \frac{1}{3} \times 3.14 \times 4^2 \times 10$$ - Calculate $4^2$: $$4^2 = 16$$ - Substitute back: $$V = \frac{1}{3} \times 3.14 \times 16 \times 10$$ - Multiply $16 \times 10$: $$V = \frac{1}{3} \times 3.14 \times 160$$ - Multiply $3.14 \times 160$: $$V = \frac{1}{3} \times 502.4$$ - Divide by 3: $$V = \cancel{\frac{1}{3}} \times 502.4 = \frac{502.4}{3}$$ $$V = 167.466\ldots$$ 4. **Final answer:** The volume of the cone is approximately $167.5$ cubic meters (rounded to the nearest tenth).