A sphere has a surface area of 314 square centimeters. What is its radius?
["# Understanding How to Calculate the Radius of a Sphere Given Its Surface Area", "When exploring three-dimensional geometry, one common question is: If a sphere has a surface area of 314 cm², what is its radius? This article provides a clear, step-by-step solution grounded in geometry, along with practical insights and relevant SEO keywords to help readers discover this topic through search engines.", "## What Is the Surface Area of a Sphere?", "The surface area ( A ) of a sphere is calculated using the formula:", "[\nA = 4\pi r^2\n]", "where:\n- ( A ) is the surface area,\n- ( r ) is the radius of the sphere,\n- ( \pi \approx 3.14 ) (Pi), a mathematical constant approximately equal to 3.14159.", "---", "## Solving for the Radius Given Surface Area", "Suppose the surface area of a sphere is 314 cm². We want to determine the radius ( r ).", "Start with the surface area formula:", "[\nA = 4\pi r^2\n]", "Plug in ( A = 314 ) cm² and ( \pi = 3.14 ):", "[\n314 = 4 \ imes 3.14 \ imes r^2\n]", "Simplify the right-hand side:", "[\n314 = 12.56 \ imes r^2\n]", "Now, solve for ( r^2 ):", "[\nr^2 = \frac{314}{12.56} = 25\n]", "Take the square root of both sides:", "[\nr = \sqrt{25} = 5\n]", "Thus, the radius of the sphere is 5 centimeters.", "---", "## Why This Matters", "Understanding how to calculate a sphere’s radius from its surface area is useful in many real-world applications, including architecture, engineering, physics, and product design. The formulas allow precise shaping and sizing, ensuring materials are used efficiently.", "---", "## SEO-Optimized Summary & Key Terms", "- Main Keywords: sphere radius calculation, surface area of sphere formula, radius of sphere with surface area\n- Long-tail Keywords: how to find radius given sphere surface area, calculate sphere radius from surface area, sphere surface area to radius formula\n- SEO Tips:\n - Include the core equation ( A = 4\pi r^2 ) with context.\n - Use reader-friendly breakdowns and step-by-step logic.\n - Mention practical relevance to increase engagement.\n - Add definitions for key terms: surface area, radius, formula.", "---", "### Final Answer", "A sphere with a surface area of 314 cm² has a radius of 5 cm.\nFormula used: ( r = \sqrt{\frac{A}{4\pi}} ) ≈ ( \sqrt{\frac{314}{12.56}} ) ≈ 5 cm.", "---", "If you’re looking to understand spherical geometry or solve similar problems, knowing this fundamental formula enables accurate and confident calculations."]
