A sphere has a surface area of 314 square centimeters. Find its radius. Use the formula \( A = 4\pi r^2 \).

["How to Find the Radius of a Sphere Given Its Surface Area: A Practical Example", "Understanding the geometry of a sphere is essential in fields ranging from physics to packaging design. One key measurement is the surface area, which relates directly to the sphere’s radius. In this article, we explore how to calculate the radius when the surface area is known—specifically, a sphere with a surface area of 314 square centimeters.", "### The Formula That Defines a Sphere’s Surface Area", "The surface area ( A ) of a sphere is determined using the formula:", "[\nA = 4\pi r^2\n]", "Where:\n- ( A ) = surface area (in square centimeters, cm²)\n- ( r ) = radius of the sphere (in centimeters, cm)\n- ( \pi ) ≈ 3.1416 (a mathematical constant used for precise calculations)", "---", "### Step-by-Step Calculation: Finding the Radius", "Given:\nSurface area ( A = 314 , \ ext{cm}^2 )", "We need to solve for the radius ( r ).", "1. Start with the surface area formula:\n[\nA = 4\pi r^2\n]", "2. Plug in the given surface area:\n[\n314 = 4\pi r^2\n]", "3. Substitute ( \pi ) with 3.1416:\n[\n314 = 4 \ imes 3.1416 \ imes r^2\n]\n[\n314 = 12.5664 \ imes r^2\n]", "4. Isolate ( r^2 ):\n[\nr^2 = \frac{314}{12.5664} \approx 25\n]", "5. Take the square root to solve for ( r ):\n[\nr = \sqrt{25} = 5\n]", "---", "### Final Answer: The Radius Is 5 cm", "If a sphere has a surface area of 314 square centimeters, its radius is exactly 5 centimeters. This relationship confirms that mathematics provides precise tools for solving real-world geometric problems—whether for scientific calculations, engineering designs, or educational purposes.", "Remember, using accurate values for ( \pi ) and following the formula ( A = 4\pi r^2 ) ensures reliable results for any sphere surface area.", "### Key Takeaways:\n- The surface area formula relates ( A ), ( r ), and ( \pi ).\n- Solving for radius involves algebraic steps and square roots.\n- A sphere with ( A = 314,\ ext{cm}^2 ) has ( r = 5,\ ext{cm} ).", "Optimized for SEO with relevant keywords: sphere surface area formula, calculate radius from surface area, how to find sphere radius, geometry formulas, math problem solution, ( A = 4\pi r^2 ), radius calculation."]