A sphere has a surface area of 314 square centimeters. Calculate its radius. Use \( \pi \approx 3.14 \).
["# How to Calculate the Radius of a Sphere with a Given Surface Area", "When studying geometry, one common problem is finding the radius of a sphere when given its surface area. The surface area of a sphere is an essential measurement in both academic and practical applications—from manufacturing spherical objects to understanding physical properties in science.", "## Understanding the Surface Area Formula", "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\n- ( \pi ) is the mathematical constant approximately equal to 3.14", "Given a sphere with a surface area of 314 square centimeters, we can solve for the radius ( r ) using this formula.", "---", "## Step-by-Step Calculation", "Step 1: Start with the surface area formula:\n[\nA = 4\pi r^2\n]", "Step 2: Substitute the given values (( A = 314 ) cm² and ( \pi \approx 3.14 )):\n[\n314 = 4 \ imes 3.14 \ imes r^2\n]", "Step 3: Simplify the right side:\n[\n314 = 12.56 \ imes r^2\n]", "Step 4: Solve for ( r^2 ) by dividing both sides by 12.56:\n[\nr^2 = \frac{314}{12.56} = 25\n]", "Step 5: Take the square root of both sides to find ( r ):\n[\nr = \sqrt{25} = 5 \ ext{ cm}\n]", "---", "## Conclusion", "A sphere with a surface area of 314 cm² has a radius of 5 centimeters. Knowing how to calculate the radius from the surface area is a key skill in geometry and helps in solving real-world problems involving spherical shapes.", "If you're ever asked to find the radius of a sphere given its surface area, recall the formula ( A = 4\pi r^2 ), use ( \pi \approx 3.14 ), solve algebraically, and verify your result. Practice helps reinforce these foundational math skills!"]
