1. **State the problem:** Find the area of a circle given its diameter is 15 cm. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $r$ is the radius of the circle. 3. **Find the radius:** The radius is half the diameter: $$r = \frac{15}{2} = 7.5 \text{ cm}$$ 4. **Calculate the area:** $$A = \pi (7.5)^2 = \pi \times 56.25 = 56.25\pi$$ 5. **Approximate the area:** Using $\pi \approx 3.1416$: $$A \approx 56.25 \times 3.1416 = 176.715$$ 6. **Round to the nearest whole number:** $$\boxed{177 \text{ cm}^2}$$