1. **State the problem:** We need to find the area of a circle with a diameter of 20 inches. 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, so: $$r = \frac{20}{2} = 10 \text{ inches}$$ 4. **Calculate the area:** Substitute $r=10$ into the area formula: $$A = \pi \times 10^2 = 100\pi$$ 5. **Approximate the area:** Using $\pi \approx 3.1416$, $$A \approx 100 \times 3.1416 = 314.16 \text{ in}^2$$ 6. **Compare with answer choices:** The closest answer is $314 \text{ in}^2$. **Final answer:** $314 \text{ in}^2$