A circle has a circumference of 31.4 cm. What is its radius? (Use \( \pi \approx 3.14 \))

["How to Calculate the Radius of a Circle Given Its Circumference – A Breakdown", "Understanding how to find the radius from a circle’s circumference is a fundamental concept in geometry. Whether you’re studying math, solving practical problems, or preparing for exams, knowing the relationship between circumference and radius is essential. In this guide, we’ll explore how to determine the radius when the circumference is 31.4 cm, using ( \pi \approx 3.14 ).", "---", "### The Basic Formula", "The circumference ( C ) of a circle is connected to its radius ( r ) by the formula:", "[\nC = 2\pi r\n]", "To find the radius, rearrange the formula:", "[\nr = \frac{C}{2\pi}\n]", "---", "### Plugging in the Known Values", "Given:\n- Circumference ( C = 31.4 ) cm\n- ( \pi \approx 3.14 )", "Substitute into the formula:", "[\nr = \frac{31.4}{2 \ imes 3.14}\n]", "First compute the denominator:", "[\n2 \ imes 3.14 = 6.28\n]", "Now divide:", "[\nr = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]", "---", "### What Does This Mean?", "If a circle has a circumference of 31.4 cm and ( \pi \approx 3.14 ), its radius is exactly 5 cm. This simple relationship shows how mathematical constants help us solve real-world geometry problems quickly and accurately.", "---", "### Why This Formula Matters", "Knowing how to calculate radius from circumference helps in countless everyday applications—designing circular objects, calculating circular tracks, creating circular layouts, and solving engineering problems. Mastering this formula ensures a strong foundation in both academic math and practical problem-solving.", "---", "Summary:\n- Circumference formula: ( C = 2\pi r )\n- For ( C = 31.4 ) cm and ( \pi \approx 3.14 ):\n [\n r = \frac{31.4}{2 \ imes 3.14} = 5 \ ext{ cm}\n ]", "---", "Final Takeaway:\nA circle with a circumference of 31.4 cm has a radius of 5 cm when using ( \pi \approx 3.14 ). This straightforward calculation highlights the elegance and utility of geometric principles in everyday life."]