A sphere has a volume of 288Ï cubic centimeters. What is its radius?
["Title: How to Find the Radius of a Sphere: Solving for a Volume of 288∏ Cubic Centimeters", "---", "When working with geometric shapes, one of the most common problems is determining key properties like volume or radius. In this article, we’ll explore how to calculate the radius of a sphere that has a volume of 288∏ cubic centimeters — a value frequently encountered in geometry, engineering, and physics.", "If you’ve ever wondered, “What is the radius of a sphere with volume 288∏ cm³?” — you’re in the right place. Let’s break down the formula, walk through the calculation step-by-step, and understand how to apply it confidently.", "---", "### Understanding the Volume Formula of a Sphere", "The volume ( V ) of a sphere is given by the formula:", "[\nV = \frac{4}{3} \pi r^3\n]", "Where:\n- ( V ) is the volume\n- ( r ) is the radius\n- ( \pi ) is the mathematical constant pi (≈3.14159)", "Given that the volume is 288∏ cm³, we substitute into the formula:", "[\n288\pi = \frac{4}{3} \pi r^3\n]", "---", "### Step-by-Step: Solving for Radius ( r )", "Start by eliminating ( \pi ) from both sides (since it appears in both terms):", "[\n288\pi \div \pi = \frac{4}{3} r^3\n]", "This simplifies to:", "[\n288 = \frac{4}{3} r^3\n]", "Now, multiply both sides by ( \frac{3}{4} ) to isolate ( r^3 ):", "[\nr^3 = 288 \ imes \frac{3}{4}\n]", "Calculate the right-hand side:", "[\nr^3 = 216\n]", "Now take the cube root of both sides to solve for ( r ):", "[\nr = \sqrt[3]{216} = 6\n]", "---", "### Final Answer", "The radius of the sphere with a volume of 288∏ cubic centimeters is:", "[\n\boxed{6 \ ext{ cm}}\n]", "---", "### Why This Formula Matters", "Understanding how to derive the radius from volume is essential in fields ranging from architecture to medicine, especially when dealing with spherical containers, droplets, or celestial bodies. The formula ( V = \frac{4}{3} \pi r^3 ) reveals how volume scales with radius — perfectly cubic with ( r^3 ).", "---", "### Summary", "- Volume formula: ( V = \frac{4}{3} \pi r^3 )\n- Substitute ( V = 288\pi )\n- Simplify: ( r^3 = 216 )\n- Solve: ( r = \sqrt[3]{216} = 6 )\n- Radius = 6 centimeters", "If you’re solving geometry problems or analyzing spherical objects, now you know how to directly compute the radius from volume — and why volume and radius are so intimately connected.", "---", "Keywords: sphere volume, radius of sphere, formula for sphere volume, how to find radius from volume, geometry problem solution, volume of sphere calculation, 288π cm³ radius, cube root sphere radius, math formula explanation", "Meta Description:\nDiscover how to calculate the radius of a sphere with volume 288∏ cm³ using the formula ( V = \frac{4}{3} \pi r^3 ). Step-by-step solution and key geometry insights. Ideal for students, engineers, and science enthusiasts.", "---", "Also read: How to Convert Sphere Volume to Radius in Real-World Applications"]
