A circle has a circumference of 31.4 meters. Find its area. (Use π ≈ 3.14)
["How to Find the Area of a Circle Given Its Circumference – A Step-by-Step Example", "Ever wondered how to calculate the area of a circle when you only know its circumference? This guide walks you through a practical example: finding the area of a circle with a circumference of 31.4 meters using an approximate value for π (π ≈ 3.14). This problem is common in geometry, engineering, architecture, and everyday measurements — making it a valuable lesson in applying math to real-world situations.", "---", "### Understanding the Relationship Between Circumference and Area", "The circumference ( C ) of a circle describes the distance around its edge, while the area ( A ) measures the space inside. These two key properties are connected through the radius ( r ), defined as the distance from the center to the edge.", "The formulae involved are:\n- Circumference: ( C = 2\pi r )\n- Area: ( A = \pi r^2 )", "Given ( C = 31.4 ) meters and approximating ( \pi ) as 3.14, we can solve for the radius and then compute the area.", "---", "### Step 1: Use Circumference to Find the Radius", "Start with the circumference formula:\n[\nC = 2\pi r\n]", "Substitute known values:\n[\n31.4 = 2 \ imes 3.14 \ imes r\n]", "Simplify:\n[\n31.4 = 6.28r\n]", "Solve for ( r ):\n[\nr = \frac{31.4}{6.28} = 5 , \ ext{meters}\n]", "---", "### Step 2: Calculate the Area Using the Radius", "Now use the area formula:\n[\nA = \pi r^2\n]", "Substitute ( r = 5 ) and ( \pi \approx 3.14 ):\n[\nA = 3.14 \ imes 5^2 = 3.14 \ imes 25 = 78.5 , \ ext{square meters}\n]", "---", "### Final Result", "A circle with a circumference of 31.4 meters has an area of 78.5 square meters when using ( \pi \approx 3.14 ).", "---", "### Why This Matters in Real Life", "This calculation isn’t just theoretical. Knowing how to derive area from circumference helps in tasks like:\n- Estimating the land area of circular plots\n- Designing round fountains, rings, or enclosures\n- Calculating material needs in construction or manufacturing", "Mastering this relationship strengthens your geometry foundation and enables smarter problem solving in both academic and professional contexts.", "---", "Keywords: circle area formula, circumference to area conversion, geometry problem-solving, circle circumference 31.4m, math tutorial, π approximation, radius calculation, real-life geometry applications."]
