1. **State the problem:** Find the diameter of a circle given its area is 415.48 square inches. 2. **Formula used:** The area $A$ of a circle is given by the formula $$A = \pi r^2$$ where $r$ is the radius. 3. **Find the radius:** Rearrange the formula to solve for $r$: $$r = \sqrt{\frac{A}{\pi}}$$ 4. **Substitute the given area:** $$r = \sqrt{\frac{415.48}{\pi}}$$ 5. **Calculate the radius:** Using $\pi \approx 3.1416$, $$r = \sqrt{\frac{415.48}{3.1416}} = \sqrt{132.25} = 11.5$$ inches 6. **Find the diameter:** Diameter $d$ is twice the radius, $$d = 2r = 2 \times 11.5 = 23$$ inches **Final answer:** The diameter of the circle is **23 inches**.