A sphere has a surface area of 144π square centimeters. What is its radius?
["# Discover the Radius of a Sphere with a Surface Area of 144π cm²", "Understanding the geometry of a sphere is essential in mathematics, physics, and engineering. One of the most common questions students and curious learners ask is: What is the radius of a sphere if its surface area is 144π square centimeters? In this SEO-optimized article, we’ll break down the formula, solve the problem step-by-step, and explain how to find the radius with clarity and precision.", "## The Surface Area Formula of a Sphere", "The surface area ( A ) of a sphere is given by the mathematical formula:", "[\nA = 4\pi r^2\n]", "where:\n- ( A ) = surface area,\n- ( r ) = radius of the sphere.", "This formula is fundamental and appears frequently in academic searches related to geometry, volume calculations, and real-world applications like engineering design and physics modeling. Optimizing for keywords such as “sphere surface area formula” ensures high relevance for students, educators, and professionals seeking accurate geometric solutions.", "## Solving for the Radius", "Given:\n[\n4\pi r^2 = 144\pi\n]", "### Step 1: Simplify the Equation", "Divide both sides of the equation by ( \pi ) (since ( \pi <br/>\neq 0 )):", "[\n4r^2 = 144\n]", "### Step 2: Solve for ( r^2 )", "Divide both sides by 4:", "[\nr^2 = \frac{144}{4} = 36\n]", "### Step 3: Take the Square Root", "Take the positive square root (since radius is a positive quantity):", "[\nr = \sqrt{36} = 6\n]", "## Conclusion", "The radius of a sphere with a surface area of ( 144\pi ) square centimeters is 6 centimeters.", "This result not only confirms theoretical knowledge but also supports practical problem-solving in fields such as architecture, manufacturing, and science. Remember, mastering formulas like this strengthens geometric understanding and improves proficiency in STEM disciplines.", "### SEO Keywords Included:\n- sphere surface area formula\n- how to find radius of a sphere\n- surface area of sphere metric\n- solve sphere radius from surface area\n- geometry problem solving techniques", "By focusing on clear explanations, step-by-step reasoning, and strategic keyword integration, this article is optimized for search engines while delivering valuable, actionable information to readers looking to understand sphere geometry efficiently.", "---", "Summary: If a sphere’s surface area is ( 144\pi , \ ext{cm}^2 ), its radius is 6 cm. Use the formula ( A = 4\pi r^2 ), simplify, solve, and take the square root to find ( r = 6 ). This foundational geometry concept enhances learning for students, teachers, and professionals alike."]
