A circle has a circumference of \( 31.4 \) cm. Calculate the radius of the circle. Use \( \pi pprox 3.14 \).
["# Understanding Circle Circumference: How to Calculate the Radius When Given ( C = 31.4 ) cm", "Circles are fundamental shapes in geometry, appearing in nature, architecture, engineering, and everyday life. One key property of a circle is its circumference—the perimeter or boundary length around the circle. If you know the circumference, you can easily determine the radius, the distance from the center to the edge. In this article, we’ll explore how to calculate the radius of a circle when given a circumference of ( 31.4 ) cm, using the approximation ( \pi \approx 3.14 ).", "## What Is the Formula for Circumference?", "The circumference ( C ) of a circle is directly related to its radius ( r ) through the formula:", "[\nC = 2\pi r\n]", "Here,\n- ( C ) is the circumference,\n- ( \pi ) (pi) is a mathematical constant approximately equal to 3.14,\n- ( r ) is the radius of the circle.", "## Step-by-Step Calculation of the Radius", "To find the radius given ( C = 31.4 ) cm and ( \pi \approx 3.14 ), follow these steps:", "1. Start with the circumference formula:", "[\nC = 2\pi r\n]", "2. Substitute the known values:", "[\n31.4 = 2 \ imes 3.14 \ imes r\n]", "3. Simplify the right-hand side:", "[\n31.4 = 6.28 \ imes r\n]", "4. Solve for ( r ) by dividing both sides by 6.28:", "[\nr = \frac{31.4}{6.28}\n]", "5. Calculate:", "[\nr = 5 \ ext{ cm}\n]", "## Final Result", "When a circle has a circumference of ( 31.4 ) cm, its radius is exactly:", "[\n\boxed{5 \ ext{ cm}}\n]", "## Why This Calculation Matters", "Knowing how to find the radius from circumference is essential not only in math but in practical applications. For example:\n- Determining the size of wheels or pipes\n- Designing circular structures like columns or jars\n- Solving problems in physics involving rotational motion\n- Everyday measurements such as calculating the hoop of a hula hoop or rope around a pole", "## Summary", "To recap:\n- Use ( C = 2\pi r )\n- Plug in ( C = 31.4 ) cm and ( \pi \approx 3.14 )\n- Solve for ( r ):\n[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]\n- Thus, a circle with a circumference of 31.4 cm has a radius of 5 cm.", "Understanding this relationship strengthens your grasp of circular geometry and supports accurate measurements in science, construction, and design.", "---", "Keywords: circle circumference, radius calculation, circumference formula, circumference to radius, ( C = 2\pi r ), ( \pi \approx 3.14 ), geometry tutorial, how to find radius, circular shape math, radius of circle with C = 31.4 cm"]
