A sphere has a volume of 288π cubic centimeters. What is the radius of the sphere?
["Title: Find the Radius of a Sphere with a Volume of 288π cm³ – Step-by-Step Calculation", "If you’ve ever wondered how to calculate the radius of a sphere given its volume, you're in the right place. Understanding sphere geometry not only enhances math skills but also plays a crucial role in fields like engineering, physics, and 3D modeling. In this article, we’ll solve a classic geometry problem: What is the radius of a sphere with a volume of 288π cubic centimeters?", "---", "### Understanding the Formula", "The volume ( V ) of a sphere is calculated using the formula:", "[\nV = \frac{4}{3} \pi r^3\n]", "Where:\n- ( V ) = volume of the sphere\n- ( r ) = radius of the sphere", "Given that the volume is ( 288\pi ) cm³, we substitute into the formula:", "[\n\frac{4}{3} \pi r^3 = 288\pi\n]", "---", "### Step-by-Step Solution", "Step 1: Eliminate π from both sides\nSince ( \pi ) appears on both sides, divide every term by ( \pi ):", "[\n\frac{4}{3} r^3 = 288\n]", "Step 2: Solve for ( r^3 )\nMultiply both sides by ( \frac{3}{4} ) to isolate ( r^3 ):", "[\nr^3 = 288 \ imes \frac{3}{4}\n]", "Calculate the right-hand side:", "[\n288 \ imes \frac{3}{4} = 216\n]", "So,", "[\nr^3 = 216\n]", "Step 3: Take the cube root\nFind ( r ) by taking the cube root of 216:", "[\nr = \sqrt[3]{216} = 6\n]", "---", "### Conclusion: The Radius is 6 Centimeters", "Thus, a sphere with a volume of ( 288\pi ) cubic centimeters has a radius of exactly 6 centimeters.", "---", "### Quick Recap", "- Volume formula: ( V = \frac{4}{3} \pi r^3 )\n- Plug in ( V = 288\pi )\n- Simplify by dividing by ( \pi )\n- Solve ( r^3 = 216 )\n- Find ( r = 6 ) cm", "---", "### Why This Matters", "Whether you're designing a physical object, analyzing pressure vessels, or studying planetary body volumes, knowing how to compute the radius from volume ensures precision and confidence in your calculations.", "If you're curious about how spheres apply in real-world applications—like measuring gas volumes, ball size in sports, or medical imaging—the math stays consistent. Mastering these foundational formulas empowers you to tackle more complex geometry with ease.", "---", "Keywords: sphere volume formula, calculate radius of sphere, sphere volume calculation, 288π cm³ sphere, geometry tutorial, find sphere radius"]
