A circle has a circumference of 31.4159 meters. Find its radius. Use \(\pi pprox 3.14159\).
["How to Find the Radius of a Circle with a Circumference of 31.4159 Meters", "Understanding the relationship between a circle’s circumference and its radius is essential in geometry, engineering, and everyday applications. If you’ve been asked to find the radius of a circle when its circumference is known, this guide will walk you through the process step-by-step—using a precise value for π and a realistic circumference of 31.4159 meters.", "### What Is Circumference and Radius?", "The circumference ( C ) of a circle is the distance around its outer edge. It is directly related to the circle’s radius ( r ) through the formula:", "[\nC = 2\pi r\n]", "where\n(\pi \approx 3.14159) (the accurate approximation commonly used),\n(C) is the circumference,\nand (r) is the radius.", "---", "### Step-by-Step Calculation", "Given:\nCircumference ( C = 31.4159 ) meters\n(\pi \approx 3.14159)", "We want to find the radius ( r ). Start with the formula:", "[\nC = 2\pi r\n]", "To solve for ( r ), rearrange the formula:", "[\nr = \frac{C}{2\pi}\n]", "Now substitute the known values:", "[\nr = \frac{31.4159}{2 \ imes 3.14159}\n]", "First, calculate the denominator:", "[\n2 \ imes 3.14159 = 6.28318\n]", "Now divide:", "[\nr = \frac{31.4159}{6.28318} = 5\n]", "---", "### Result and Conclusion", "The radius of the circle is exactly 5 meters.", "This matches perfectly with real-world geometry, since a circle with ( \pi = 3.14159 ) and circumference ( 2 \ imes 3.14159 \ imes 5 = 31.4159 ) meters is accurate and easy to verify.", "---", "### Why This Matters", "Whether designing circular structures, calculating materials, or solving physics problems, knowing how to deduce radius from circumference saves time and reduces errors. Using (\pi \approx 3.14159) ensures reliable results without excessive rounding.", "Bottom line: If a circle has a circumference of 31.4159 meters and (\pi \approx 3.14159), then its radius is precisely 5 meters."]
