A circle has a circumference of 31.4 cm. Calculate its radius and area.
["# How to Calculate the Radius and Area of a Circle with a Circumference of 31.4 cm", "Understanding the basic geometry of a circle is essential for students, engineers, and anyone dealing with measurements in real life. One of the most common questions is: if a circle has a circumference of 31.4 cm, what is its radius and area? In this article, we’ll walk you through the step-by-step calculation using fundamental circle formulas, helping you solve similar problems with confidence.", "## What Is Circumference?", "The circumference of a circle is the total distance around its outer edge. A key formula relating circumference to radius is:", "[\nC = 2\pi r\n]", "Where:\n- ( C ) = circumference\n- ( r ) = radius (the distance from the center to the edge)\n- ( \pi ) (pi) ≈ 3.14", "Given that the circumference ( C = 31.4 ) cm, we can solve for the radius ( r ).", "---", "## Step 1: Calculate the Radius", "Using the formula:\n[\nC = 2\pi r\n]", "Substitute the known value:\n[\n31.4 = 2 \ imes 3.14 \ imes r\n]", "Simplify:\n[\n31.4 = 6.28 \ imes r\n]", "Now, solve for ( r ):\n[\nr = \frac{31.4}{6.28} = 5 , \ ext{cm}\n]", "✅ So, the radius of the circle is 5 centimeters.", "---", "## Step 2: Calculate the Area", "The area ( A ) of a circle is calculated using the formula:\n[\nA = \pi r^2\n]", "Substitute ( r = 5 ) cm:\n[\nA = 3.14 \ imes (5)^2 = 3.14 \ imes 25 = 78.5 , \ ext{cm}^2\n]", "---", "## Final Results", "- Radius: 5 cm\n- Circumference: 31.4 cm\n- Area: 78.5 cm²", "---", "## Why Knowing This Matters", "Whether you're designing a garden bed, a wheel, or analyzing circular structures, knowing how to compute radius and area from circumference is key. These calculations help in planning, measuring materials, and solving real-world geometry problems efficiently.", "---", "Q: Can I use 22/7 instead of 3.14 for more precision?\nYes, ( \frac{22}{7} \approx 3.142857 ), which gives a slightly more accurate circumference for ( r = 5 ):\n( C = 2 \ imes \frac{22}{7} \ imes 5 = \frac{220}{7} \approx 31.4286 ) cm — very close to 31.4 cm.", "For classroom purposes or quick estimation, 3.14 is standard; for advanced use, ( \frac{22}{7} ) or ( \pi ) symbol gives greater accuracy.", "---", "If you found this guide helpful, share it to help others master circle geometry — because math should be clear, intuitive, and easy to apply! 🔄", "---", "### Summary\n- Use ( r = \frac{C}{2\pi} ) to find radius.\n- Use ( A = \pi r^2 ) to calculate area.\n- Circle circumference = 31.4 cm ⇒ radius = 5 cm, area = 78.5 cm².\n- Use ( \pi \approx 3.14 ) or fraction ( \frac{22}{7} ) for calculations."]
