Solve for \( r \): \( 31.4 = 2 \times 3.14 \times r \) → \( r = 5 \) cm

["Solve for ( r ): ( 31.4 = 2 \ imes 3.14 \ imes r ) → ( r = 5 ) cm", "Understanding how to solve for a variable in a simple linear equation is a fundamental skill in math and science. One common problem you may encounter involves relating area or volume using a constant like ( \pi ). In this article, we’ll walk through how to solve the equation ( 31.4 = 2 \ imes 3.14 \ imes r ), ultimately finding that ( r = 5 ) cm. This step-by-step guide is perfect for students, teachers, and anyone looking to master solving basic algebraic expressions.", "---", "### Step 1: Recognize the Equation Structure", "The equation ( 31.4 = 2 \ imes 3.14 \ imes r ) represents a proportional relationship. Here, ( 2 \ imes 3.14 ) calculates part of the constant area or volume coefficient, and ( r ) is the unknown measurement we need to find.", "---", "### Step 2: Simplify the Right Side", "First, calculate the product of the constants on the right side:", "[\n2 \ imes 3.14 = 6.28\n]", "Now, the equation becomes:", "[\n31.4 = 6.28 \ imes r\n]", "---", "### Step 3: Isolate the Variable ( r )", "To solve for ( r ), divide both sides of the equation by ( 6.28 ):", "[\nr = \frac{31.4}{6.28}\n]", "---", "### Step 4: Perform the Division", "Carrying out the division:", "[\nr = 5\n]", "This means the unknown radius ( r ) is exactly 5 centimeters.", "---", "### Real-World Application: Relating Area and Radius", "This type of equation often appears in geometry, especially when dealing with the area of a circle. Recall the formula:", "[\n\ ext{Area} = \pi \ imes r^2\n]", "For a circle with radius ( r ), if we know the area is 31.4 square centimeters and we use ( \pi \approx 3.14 ), setting up the equation:", "[\n31.4 = 3.14 \ imes r^2\n]", "If the formula had simplified to ( 31.4 = 2 \ imes 3.14 \ imes r ), that suggests a context emphasizing multiplication of constants with radius—common in scaled problems or derived formulas where ( 2 \ imes 3.14 ) approximates effective radius scaling.", "Solving gives:", "[\nr^2 = \frac{31.4}{6.28} = 5 \quad \Rightarrow \quad r = \sqrt{5} \approx 5 \ ext{ cm (approximate)}\n]", "But if the context uses the simplified equation directly (as in the original), then clearly:", "[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]", "---", "### Quick Summary:", "- The equation ( 31.4 = 2 \ imes 3.14 \ imes r ) simplifies to ( 31.4 = 6.28 \ imes r )\n- Dividing both sides by 6.28 yields ( r = 5 )\n- This result is consistent with the area formula when accounting for constant scaling\n- Understanding variable isolation is essential for solving geometry problems efficiently", "---", "### Call to Action", "Need more practice? Try solving similar equations like:", "- ( 28.26 = 3 \ imes 3.14 \ imes r )\n- Practice applying algebra to real-life problems involving circles, cylinders, and spheres!", "Mastering basic algebra today lays the foundation for advanced math, science, and engineering challenges tomorrow.", "---", "Keywords: solve for ( r ), equation solving, circle radius, ( 2 \ imes 3.14 \ imes r = 31.4 ), algebra tutorial, geometry formulas, radius calculation, ( \pi ) constant, math problem explanation."]