1. **Problem:** Diana is painting a circular mural with a diameter of 7 feet. Find the area she will paint. 2. **Formula:** The area $A$ of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Step 1:** Find the radius from the diameter. $$r = \frac{d}{2} = \frac{7}{2} = 3.5 \text{ feet}$$ 4. **Step 2:** Calculate the area using the radius. $$A = \pi (3.5)^2 = \pi \times 12.25 = 12.25\pi$$ 5. **Step 3:** Approximate the area using $\pi \approx 3.1416$. $$A \approx 12.25 \times 3.1416 = 38.48 \text{ square feet}$$ 6. **Answer:** Diana will paint approximately **38.48 square feet** of wall space.