A circle is inscribed in a square with side length 10 cm. What is the area of the region inside the square but outside the circle?
["Title: How to Calculate the Area Inside a Square but Outside an Inscribed Circle: A Step-by-Step Guide", "When a circle is perfectly inscribed inside a square, the geometry becomes both elegant and practical—especially in math problems. In this article, we explore a classic scenario: a circle inscribed in a square with a side length of 10 cm and determine the area of the region that lies inside the square but outside the circle.", "---", "### What Does It Mean for a Circle to Be Inscribed in a Square?", "An inscribed circle touches all four sides of the square evenly. This means the diameter of the circle equals the side length of the square. Since the square’s side is 10 cm, the circle’s diameter is also 10 cm, giving it a radius of:", "[\n\ ext{Radius} = \frac{10}{2} = 5, \ ext{cm}\n]", "---", "### Step-by-Step: How to Find the Area Inside the Square but Outside the Circle", "Step 1: Calculate the Area of the Square\nArea of a square = side²\n[\n\ ext{Area}{\ ext{square}} = 10^2 = 100, \ ext{cm}^2\n]", "Step 2: Calculate the Area of the Inscribed Circle\nArea of a circle = π × radius²\n[\n\ ext{Area}^2}} = \pi \ imes 5^2 = 25\pi, \ ext{cm\n]", "Step 3: Subtract to Find the Desired Area\nThe region inside the square but outside the circle is the difference between the square’s area and the circle’s area:\n[\n\ ext{Desired Area} = \ ext{Area}{\ ext{square}} - \ ext{Area} = 100 - 25\pi}\n]", "Since π ≈ 3.1416, you can approximate:\n[\n25\pi \approx 25 \ imes 3.1416 = 78.54, \ ext{cm}^2\n]\n[\n\ ext{Desired Area} \approx 100 - 78.54 = 21.46, \ ext{cm}^2\n]", "But for exactness, the precise answer is:\n[\n\boxed{100 - 25\pi}, \ ext{cm}^2\n]", "---", "### Why This Formula Matters", "Understanding how to compute the area between shapes like squares and inscribed circles is fundamental in geometry, architecture, design, and engineering. It helps estimate materials, design layouts, and solve real-world puzzles involving space optimization.", "---", "### Final Summary", "- A circle inscribed in a 10 cm square has radius 5 cm\n- The square’s area = 100 cm²\n- The circle’s area ≈ 78.54 cm²\n- The area between the square and circle = 100 – 25π ≈ 21.46 cm²", "This simple yet powerful example illustrates how geometry transforms abstract shapes into practical calculations—ideal for students, teachers, and anyone curious about math in everyday life.", "---", "Keywords: circle inscribed in square, area of square minus circle, inscribed circle formula, area inside square but outside circle, 10 cm square area calculation\nMeta Description: Learn how to find the area inside a 10 cm square but outside the inscribed circle using basic geometry. Step-by-step solution with formula and explanation."]
