A circle’s circumference is 31.4 meters. What is its area?
["Understanding Circle Geometry: Calculating Area When Circumference is Known", "When you know the circumference of a circle, determining its area is straightforward using fundamental formulas in geometry. This article explains how to find the area of a circle when its circumference is given—using a specific example: a circle with a circumference of 31.4 meters—so you can easily grasp the process for any circular object or structure.", "---", "### Given\nCircumference = 31.4 meters", "---", "### Step 1: Recall the Formula for Circumference\nThe circumference ( C ) of a circle is calculated using the formula:\n[\nC = 2\pi r\n]\nwhere ( r ) is the radius.", "---", "### Step 2: Solve for the Radius\nWe are given ( C = 31.4 , \ ext{m} ). Rearranging the formula to solve for radius:\n[\nr = \frac{C}{2\pi}\n]\nUsing ( \pi \approx \frac{22}{7} ),\n[\nr = \frac{31.4}{2 \ imes \frac{22}{7}} = \frac{31.4 \ imes 7}{2 \ imes 22} = \frac{219.8}{44} = 4.995 \approx 5 , \ ext{meters}\n]\n(Note: This approximation gives ( r \approx 5 ) meters, which aligns well with common design or real-world round numbers.)", "---", "### Step 3: Use Area Formula\nThe area ( A ) of a circle is:\n[\nA = \pi r^2\n]\nSubstituting ( r = 5 , \ ext{m} ):\n[\nA = \pi \ imes 5^2 = 25\pi\n]\nUsing ( \pi \approx 3.14 ),\n[\nA \approx 25 \ imes 3.14 = 78.5 , \ ext{square meters}\n]", "---", "### Final Answer\nThe area of a circle with a circumference of 31.4 meters is approximately 78.5 square meters.", "---", "### Why This Matters\nUnderstanding how to calculate area from circumference is essential in fields like engineering, architecture, landscaping, and manufacturing—where precise space planning is crucial. Whether working with circular pools, wheels, plates, or domes, geometry forms the foundation for accurate design and cost estimation.", "Key Takeaways:\n- Circumference helps find the radius\n- Radius enables area calculation via ( A = \pi r^2 )\n- Approximations using ( \pi \approx 3.14 ) or ( \frac{22}{7} ) yield reliable results in practical applications", "---", "FAQ: How do I calculate area when I only know circumference?\n1. Use ( r = \frac{C}{2\pi} )\n2. Then compute ( A = \pi r^2 )\n3. Substitute ( r ) and simplify with the value of ( \pi )", "---", "Optimizing your circle-related calculations helps ensure precision and efficiency—whether solving exercises or tackling real-world problems."]
