A circle has a circumference of 31.4 cm. Find its radius.
["# How to Find the Radius of a Circle with a Given Circumference", "Understanding how to calculate the radius from a circle’s circumference is a fundamental skill in geometry. Whether you're studying for exams, solving real-world problems, or working in design and engineering, knowing this formula helps you uncover essential geometric relationships. In this article, we’ll explore how to find the radius of a circle when the circumference is known—using a practical example: if the circumference is 31.4 cm, what is the radius?", "## What Is Circumference?", "The circumference of a circle is the total distance around its edge. It relates directly to the circle’s radius—the distance from the center of the circle to any point on its edge. The formula that connects these two measurements is:", "[\nC = 2\pi r\n]", "where:\n- ( C ) = circumference\n- ( r ) = radius\n- ( \pi ) (pi) is a mathematical constant approximately equal to 3.14", "## Calculating the Radius from Circumference", "To find the radius (( r )) when you know the circumference (( C )), you can rearrange the formula:", "[\nr = \frac{C}{2\pi}\n]", "Substituting the given value of ( C = 31.4 ) cm:", "[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]", "Thus, the radius of the circle is 5 cm.", "## Verifying the Result", "To confirm, we can reverse the calculation. Multiply the radius by 2 and then by ( \pi ):", "[\n2 \ imes 5 \ imes 3.14 = 31.4 \ ext{ cm}\n]", "The result matches the given circumference, verifying that the radius is correct.", "## Why This Formula Matters", "Using ( r = \frac{C}{2\pi} ) is essential in fields like architecture, physics, manufacturing, and daily life—from designing circular structures to estimating distances along pathways. Knowing the radius lets you compute area (( A = \pi r^2 )) and diameter (( d = 2r )), expanding the circle’s practical applications.", "## Step-by-Step Summary", "- Start with the circumference: ( C = 31.4 ) cm\n- Use the formula ( r = \frac{C}{2\pi} )\n- Plug in values: ( r = \frac{31.4}{2 \ imes 3.14} )\n- Calculate: ( r = \frac{31.4}{6.28} = 5 ) cm\n- Confirm by computing ( 2\pi r \approx 31.4 ) cm — it checks out!", "## Final Answer", "A circle with a circumference of 31.4 cm has a radius of 5 cm.", "---", "By mastering this basic formula, you’ve unlocked a key tool in geometry—enabling you to solve countless related problems with confidence. Whether for schoolwork or real-world tasks, knowing how to find the radius from circumference strengthens your mathematical foundation."]
