A company produces circular drink coasters. The equation x2 + y2 = 18.0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece?

In the equation x² + y² = 18.0625, the radius squared is 18.0625, so the coaster’s radius is 4.25 inches. The smallest square that can contain the circular coaster has side length equal to its diameter: 2 × 4.25 = 8.5 inches. Its area is 8.5² = 72.25 square inches, so the minimum area is 72.25 in².

AI-written and checked against the verified answer.