1. **State the problem:** We need to find the volume of a cylindrical pole with height $20$ m and base radius $7$ m. 2. **Formula used:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Substitute the values:** $$V = \pi \times 7^2 \times 20$$ 4. **Calculate the square of the radius:** $$7^2 = 49$$ 5. **Multiply all terms:** $$V = \pi \times 49 \times 20 = 980\pi$$ 6. **Approximate the volume:** Using $\pi \approx 3.1416$, $$V \approx 980 \times 3.1416 = 3078.76$$ 7. **Final answer:** The volume of the cylindrical pole is approximately $3078.76$ cubic meters.