Solve for radius \( r \): \( r = 31.4 / (2\pi) = 5 \) meters.

["Solving for Radius: Simplifying the Formula ( r = \frac{31.4}{2\pi} = 5 ) Meters", "Understanding the relationship between a circle’s circumference and its radius is fundamental in geometry—and solving for ( r ) is a clear example of applying that connection. The equation ( r = \frac{31.4}{2\pi} = 5 ) meters provides a straightforward way to find the radius when the circumference is known, making it both a practical and educational example.", "### What Is the Formula for Circumference?", "The circumference ( C ) of a circle is calculated using the formula:\n[\nC = 2\pi r\n]\nwhere ( r ) is the radius, and ( \pi ) (pi) is a mathematical constant approximately equal to 3.14. This formula describes how the distance around a circle relates to its radius — as the radius increases, so does the circumference linearly proportional to ( \pi r ).", "### Solving for Radius", "To find the radius, rearrange the formula:\n[\nr = \frac{C}{2\pi}\n]\nGiven the numerical example where ( C = 31.4 ) meters:\n[\nr = \frac{31.4}{2\pi}\n]\nUsing ( \pi \approx 3.14 ), plug in the values:\n[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ meters}\n]", "### Why This Matters", "Expressing ( r = \frac{31.4}{2\pi} = 5 ) meters helps students and practitioners quickly find the circle’s radius without memorizing the full formula. It demonstrates how real-world measurements (like a circumference of 31.4 meters) connect directly to geometric calculations, supporting engineering, architecture, and design.", "### Final Takeaway", "This simple algebraic rearrangement — transforming circumference into radius using ( r = \frac{C}{2\pi} ) — highlights a core principle in geometry. The result ( r = 5 ) meters emerges naturally from ( C = 31.4 ) meters, making it an essential technique to master for solving circular measurements efficiently. Whether measuring pipes, wheels, or circular plots, understanding how to solve for radius is invaluable.", "---", "Keywords: radius formula, solve for radius, circumference to radius, solve ( r ), geometry simplification, how to find circle radius, solve ( r = 31.4 / (2\pi) ), 5 meter circle, math explanation, geometry reference.", "Meta Description: Learn how to solve ( r = \frac{31.4}{2\pi} = 5 ) using the circle circumference formula. Discover step-by-step geometry simplification and real-world applications for radius calculations."]