1. **State the problem:** We need to find the area of land covered by an irrigation arm that acts as the radius of a circular irrigation system with radius $r = 390$ ft. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $r$ is the radius. 3. **Substitute the radius:** $$A = \pi (390)^2$$ 4. **Calculate the square:** $$390^2 = 390 \times 390 = 152100$$ 5. **Write the exact area in terms of $\pi$:** $$A = 152100 \pi$$ 6. **Interpretation:** The land covered by the irrigation arm is exactly $152100 \pi$ square feet. This matches the given answer and is the exact area in terms of $\pi$.