Question**: A circle has a circumference of 31.4 cm. Find its area using π = 3.14.

["# How to Find the Area of a Circle When Given Circumference: A Step-by-Step Guide", "Understanding the area of a circle based on its circumference is a fundamental concept in geometry, widely applied in engineering, design, and everyday measurements. In this article, we’ll explore how to calculate a circle’s area when its circumference measures 31.4 cm, using the approximation π = 3.14, which enhances learning and practical calculations.", "---", "## The Relationship Between Circumference and Area", "The circumference of a circle directly relates to its radius through the formula:\n[\nC = 2\pi r\n]\nwhere:\n- ( C ) = circumference\n- ( r ) = radius\n- ( \pi ) — pi, approximately 3.14", "Given the circumference ( C = 31.4 , \ ext{cm} ), we can solve for the radius, then use it to find the area with the formula:\n[\nA = \pi r^2\n]", "---", "## Step-by-Step Calculation", "### Step 1: Find the radius", "Using the circumference formula:\n[\nC = 2\pi r\n]\nSubstitute ( C = 31.4 ) cm and ( \pi = 3.14 ):\n[\n31.4 = 2 \ imes 3.14 \ imes r\n]\n[\n31.4 = 6.28r\n]\nNow, solve for ( r ):\n[\nr = \frac{31.4}{6.28} = 5 , \ ext{cm}\n]", "### Step 2: Calculate the area", "Now that we know the radius is 5 cm, use the area formula:\n[\nA = \pi r^2 = 3.14 \ imes 5^2 = 3.14 \ imes 25 = 78.5 , \ ext{cm}^2\n]", "---", "## Final Answer", "The area of the circle with a circumference of 31.4 cm is 78.5 cm².", "---", "## Why This Matters", "Knowing how to compute area from circumference helps in solving real-world problems such as determining the size of circular plots, pipes, medals, or lenses—common in architecture, manufacturing, and scientific studies. Using ( \pi = 3.14 ) makes mental math and classroom calculations more accessible, while understanding the underlying formulas builds stronger problem-solving skills.", "---", "## Key Takeaways", "- Use ( C = 2\pi r ) to find radius from circumference.\n- Substitute radius into ( A = \pi r^2 ) to find area.\n- Approximate ( \pi = 3.14 ) for quick, precise results.\n- Circumference = 31.4 cm → radius = 5 cm → area = 78.5 cm²", "---", "Ready to calculate your circle’s area? Use the same method with any circumference value, and leverage ( \pi = 3.14 ) for fast, reliable results!"]