Résolvons pour \( r \): \( 2\pi r = 31.4 \).
["# Résolvons pour ( r ): ( 2\pi r = 31.4 ) — How to Solve for Radius Using Circumference", "Understanding the fundamental relationship between circumference and radius is essential in mathematics, physics, and engineering. Have you ever asked yourself, “Résolvons pour ( r ): ( 2\pi r = 31.4 )?” This equation is a practical example of finding the radius of a circle when given the circumference — a common problem with real-world applications ranging from construction to physics.", "## The Core Equation: Circumference Formula", "The circumference ( C ) of a circle is defined by the formula:", "[\nC = 2\pi r\n]", "where:\n- ( C ) is the circumference,\n- ( r ) is the radius,\n- ( \pi ) (pi) is a constant approximately equal to 3.1416.", "Given a known circumference of ( 31.4 ), our goal is to solve for ( r ):", "[\n2\pi r = 31.4\n]", "## Step-by-Step Solution", "### Step 1: Isolate ( r )", "To solve for ( r ), divide both sides of the equation by ( 2\pi ):", "[\nr = \frac{31.4}{2\pi}\n]", "### Step 2: Plug in the Value of ( \pi )", "Using the commonly accepted approximation ( \pi \approx 3.14 ), we substitute:", "[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28}\n]", "### Step 3: Perform the Calculation", "Now divide:", "[\nr \approx \frac{31.4}{6.28} = 5\n]", "Thus, the radius is:", "[\n\boxed{5}\n]", "## Why This Calculation Matters", "Knowing how to solve linear equations involving ( \pi r ) helps in determining circular dimensions in real-life scenarios such as:", "- Calculating the radius of tires, pipes, or circular platforms.\n- Analyzing the size of planetary orbits in simplified models.\n- Working on geometry problems related to sports fields, wheels, and architecture.", "## Summary: Key Takeaway", "To solve for ( r ) in ( 2\pi r = 31.4 ), simply divide 31.4 by ( 2\pi ). The radius is exactly 5 units. This straightforward algebraic manipulation reflects the power of basic geometry combined with numerical precision.", "---", "### External SEO Optimization Keywords:\n- Solve ( 2\pi r = 31.4 )\n- Formula solver radius from circumference\n- Circumference to radius calculation\n- How to find radius with given circumference\n- Math example: ( 2\pi r = 31.4 ) solution\n- Solve ( r = \frac{31.4}{2\pi} ", "Including these terms strengthens SEO value when targeting educational searches about geometry or algebra solutions.", "---", "Further Reading:\n- How to Calculate Circumference Easily\n- Real-World Applications of Circle Formulas\n- Understanding Pi (( \pi )) in Everyday Math", "---", "Visit our blog for more step-by-step math tutorials and science-based problem solving."]
