Question:** A circle is inscribed in a square with side length 10 cm. What is the area of the shaded region outside the circle but inside the square, expressed in terms of \(\pi\)?

["Understanding the Area of the Shaded Region Between a Circle and a Square", "When a circle is inscribed inside a square, the circle touches all four sides of the square, making it perfectly symmetrical. This problem explores a classic geometric scenario: finding the area of the shaded region that lies between the square and the inscribed circle—often referred to as the shaded annular region.", "Given:\n- A square with side length = 10 cm\n- A circle inscribed in the square (fitting exactly within the square, tangent to all sides)", "---", "### Step 1: Calculate the Area of the Square\nThe area of a square is calculated using the formula:\n[\n\ ext{Area}{\ ext{square}} = \ ext{side}^2 = 10^2 = 100 \ ext{ cm}^2\n]", "---", "### Step 2: Calculate the Radius and Area of the Inscribed Circle\nSince the circle is inscribed in the square, its diameter equals the side length of the square.\n[\n\ ext{Diameter} = 10 \ ext{ cm} \Rightarrow \ ext{Radius} = \frac{10}{2} = 5 \ ext{ cm}\n]", "Using the area formula for a circle:\n[\n\ ext{Area}^2}} = \pi r^2 = \pi (5)^2 = 25\pi \ ext{ cm\n]", "---", "### Step 3: Compute the Area of the Shaded Region\nThe shaded region lies between the square and the circle. Its area is the difference between the area of the square and the area of the circle:\n[\n\ ext{Area}{\ ext{shaded}} = \ ext{Area}^2}} - \ ext{Area}_{\ ext{circle}} = 100 - 25\pi \ ext{ cm\n]", "---", "### Final Answer\nThe area of the shaded region outside the circle but inside the square is:\n[\n\boxed{100 - 25\pi \ ext{ cm}^2}\n]", "This elegant expression, in terms of (\pi), highlights the relationship between linear dimensions and curved area, commonly encountered in geometry and mathematics education."]