1. **Problem statement:** A farmer has tethered his cow with a rope 9 metres long. We need to find the maximum grazing area available to the cow. 2. **Formula used:** The maximum grazing area is the area of a circle with radius equal to the length of the rope. The area $A$ of a circle is given by: $$A = \pi r^2$$ where $r$ is the radius. 3. **Applying the formula:** Here, $r = 9$ metres. So, $$A = \pi \times 9^2 = \pi \times 81 = 81\pi$$ 4. **Calculating the numerical value:** Using $\pi \approx 3.1416$, $$A \approx 81 \times 3.1416 = 254.47$$ 5. **Conclusion:** The maximum grazing area of the cow is approximately $254.47$ square metres.