1. **State the problem:** We need to find the area of a circle with radius $r = 3$ cm. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $\pi$ is approximately 3.1416. 3. **Calculate the area:** Substitute $r = 3$ cm into the formula: $$A = \pi \times 3^2 = \pi \times 9$$ 4. **Evaluate:** $$A = 3.1416 \times 9 = 28.2744$$ 5. **Round the answer:** The area is approximately $28.26$ cm$^2$. **Final answer:** $28.26$ cm$^2$