A sphere has a volume of 288π cubic centimeters. What is the radius of the sphere? (Use \( V = \frac{4}{3}\pi r^3 \))

["How to Find the Radius of a Sphere Given Its Volume (288π cm³)", "If you’re curious about the radius of a sphere when its volume is known, you’ve come to the right place. In this article, we’ll walk you through a practical solution using the standard formula for the volume of a sphere:\n[\nV = \frac{4}{3}\pi r^3\n]\nGiven that the volume is ( 288\pi ) cubic centimeters, we’ll solve step by step to find the radius.", "---", "### Understanding the Sphere Volume Formula", "The volume ( V ) of a sphere depends on its radius ( r ) and is calculated using:\n[\nV = \frac{4}{3}\pi r^3\n]", "This formula comes from integrating the volume of circular slices from the center to the surface. Knowing this formula allows us to find the radius when volume is given—exactly the problem we’re solving.", "---", "### Step-by-Step Calculation", "Given:\n[\nV = 288\pi \ ext{ cm}^3\n]\nUsing the volume formula:\n[\n288\pi = \frac{4}{3}\pi r^3\n]", "Step 1: Eliminate ( \pi ) from both sides\nSince ( \pi ) appears on both sides, divide both equations by ( \pi ):\n[\n288 = \frac{4}{3}r^3\n]", "Step 2: Solve for ( r^3 )\nMultiply both sides by 3 to eliminate the fraction:\n[\n3 \ imes 288 = 4r^3 \quad \Rightarrow \quad 864 = 4r^3\n]\nThen divide by 4:\n[\nr^3 = \frac{864}{4} = 216\n]", "Step 3: Take the cube root\nTo find ( r ), take the cube root of 216:\n[\nr = \sqrt[3]{216} = 6\n]", "---", "### Final Answer", "The radius of a sphere with a volume of ( 288\pi ) cubic centimeters is 6 centimeters.", "---", "### Summary", "- The sphere’s volume formula is ( V = \frac{4}{3}\pi r^3 )\n- Given ( V = 288\pi ), dividing by ( \pi ) simplifies the equation\n- Solving Algebraically:\n [\n r^3 = 216 \quad \Rightarrow \quad r = 6 \ ext{ cm}\n ]\n- This confirms the radius is exactly 6 cm.", "Knowing how to apply the volume formula makes it easy to find any missing dimension of a sphere—perfect for geometry practice, science experiments, or real-world applications like balloons, soup cans, or astronomical modeling.", "If you want to find the volume from a known radius or vice versa, just plug values into ( V = \frac{4}{3}\pi r^3 ) with consistent units!", "---", "Keywords: sphere volume, calculate sphere radius, volume of a sphere formula, solve for radius, ( V = \frac{4}{3}\pi r^3 ), geometry problems, cubic meter calculations, radius from volume, mathematical formula."]