1. **State the problem:** We need to find the diameter of a piston given its area is 57.02 square inches. 2. **Formula used:** The area $A$ of a circle is given by the formula $$A = \pi \left(\frac{d}{2}\right)^2$$ where $d$ is the diameter. 3. **Rearrange the formula to solve for diameter $d$:** $$A = \pi \frac{d^2}{4}$$ Multiply both sides by 4: $$4A = \pi d^2$$ Divide both sides by $\pi$: $$\frac{4A}{\pi} = d^2$$ Taking the square root of both sides: $$d = \sqrt{\frac{4A}{\pi}}$$ 4. **Substitute the given area $A = 57.02$:** $$d = \sqrt{\frac{4 \times 57.02}{\pi}}$$ 5. **Calculate the value:** $$d = \sqrt{\frac{228.08}{3.1416}} = \sqrt{72.60}$$ 6. **Final diameter:** $$d \approx 8.52$$ inches (rounded to the nearest hundredth) Therefore, the diameter of the piston is approximately **8.52 inches**.