To find the radius \( r \), use the formula for circumference:

["# How to Find the Radius ( r ): Using the Circumference Formula Explained", "Understanding the relationship between a circle’s circumference and its radius is essential in geometry. Whether you're solving math problems, working on engineering tasks, or simply exploring real-world applications, knowing how to calculate the radius from the circumference is a fundamental skill.", "## The Key Formula: Circumference and Radius", "The circumference ( C ) of a circle is directly related to its radius ( r ) through the well-known formula:", "[\nC = 2\pi r\n]", "Here, ( \pi ) (pi) is a mathematical constant approximately equal to 3.14159, representing the ratio of a circle’s circumference to its diameter. This simple yet powerful equation allows you to determine the circle's radius when the circumference is known.", "## How to Find the Radius ( r )", "To find the radius ( r ), rearrange the formula to solve for ( r ):", "[\nr = \frac{C}{2\pi}\n]", "This transformation makes it straightforward: simply divide the given circumference ( C ) by twice the value of ( \pi ), and you’ve found the radius.", "### Step-by-Step Example", "Suppose the circumference of a circle is ( C = 31.4 ) cm. Using the formula:", "[\nr = \frac{31.4}{2\pi} = \frac{31.4}{6.2832} \approx 5 \ ext{ cm}\n]", "So, the radius is approximately 5 cm.", "## Why This Formula Matters", "Using the circumference to find the radius is vital not just in theoretical math, but also in practical contexts:", "- Design and manufacturing: Ensuring circular parts fit precise dimensions\n- Construction: Calculating material needs for cylindrical structures\n- Environmental science: Estimating the boundaries of circular plots of land or water bodies\n- Everyday calculation: From grades in sports fields to packaging dimensions", "## Summary", "To find the radius ( r ) from the circumference ( C ):", "[\n\boxed{r = \frac{C}{2\pi}}\n]", "This simple formula unlocks precise measurements and enhances problem-solving in geometry and beyond.", "---", "Keywords: radius formula, circumference to radius, geometry calculations, circle radius formula, C = 2πr, apply circumference, circular measurements, math help"]