1. **State the problem:** We are given a circle with an area of 16 square inches and need to find its diameter. 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:** Since $A = 16$, substitute into the formula: $$16 = \pi r^2$$ Divide both sides by $\pi$: $$r^2 = \frac{16}{\pi}$$ Take the square root of both sides: $$r = \sqrt{\frac{16}{\pi}} = \frac{4}{\sqrt{\pi}}$$ 4. **Find the diameter:** The diameter $d$ is twice the radius: $$d = 2r = 2 \times \frac{4}{\sqrt{\pi}} = \frac{8}{\sqrt{\pi}}$$ 5. **Calculate the numerical value:** Using $\pi \approx 3.1416$, $$d \approx \frac{8}{\sqrt{3.1416}} = \frac{8}{1.7725} \approx 4.51$$ 6. **Final answer:** The diameter of the circle is approximately **4.51 inches**.