The volume of a cylinder is \(288\pi\) cm\(^3\) and its height is 12 cm. Find the radius.
["Title: How to Find the Radius of a Cylinder Given Its Volume and Height | Step-by-Step Guide", "Meta Description:\nLearn how to calculate the radius of a cylinder when the volume and height are known. We’ll solve for the radius using the formula ( V = \pi r^2 h ) with real examples and clear explanations.", "---", "### Understanding the Volume of a Cylinder", "When dealing with cylindrical objects—whether a can, a pipe, or a storage tank—knowing the relationship between volume, radius, and height is essential. The formula to compute the volume ( V ) of a cylinder is:", "[\nV = \pi r^2 h\n]", "where:\n- ( V ) = volume (in cm³)\n- ( r ) = radius (in cm)\n- ( h ) = height (in cm)", "In this article, we’ll explore how to determine the radius when the volume and height are given. Let’s use a practical example to illustrate the process.", "### Given Values", "According to the problem:\n- Volume ( V = 288\pi ) cm³\n- Height ( h = 12 ) cm", "Our goal: Find the radius ( r ).", "### Step-by-Step Calculation", "Start with the volume formula:\n[\nV = \pi r^2 h\n]", "Substitute the known values:\n[\n288\pi = \pi r^2 \cdot 12\n]", "Divide both sides by ( \pi ) to simplify:\n[\n288 = 12 r^2\n]", "Now divide both sides by 12:\n[\nr^2 = \frac{288}{12} = 24\n]", "Finally, take the square root of both sides to solve for ( r ):\n[\nr = \sqrt{24} = \sqrt{4 \ imes 6} = 2\sqrt{6}\n]", "So, the radius of the cylinder is ( 2\sqrt{6} ) cm.", "### Why Knowing the Radius Matters", "Understanding the radius helps in real-world applications like manufacturing, construction, and packaging design. Whether you're calculating material needs, comparing cylinder sizes, or troubleshooting dimensional flaws, the radius is a key measurement.", "### Summary", "To find the radius of a cylinder from its volume and height:\n1. Use the volume formula ( V = \pi r^2 h )\n2. Substitute known values\n3. Solve algebraically for ( r )\n4. Simplify using square roots as needed", "In this case:\n- Volume: ( 288\pi ) cm³\n- Height: 12 cm\n- Radius: ( r = 2\sqrt{6} ) cm ≈ 4.899 cm", "Now you know how to accurately compute the radius once you understand the volume and height relationship.", "---", "Keywords: radius of cylinder, volume of cylinder formula, calculate cylinder radius, how to find cylinder radius, cylinder volume calculation, ( V = \pi r^2 h ", "Ready to solve your geometry problems? Use this method whenever you’re given volume and height to find the missing radius!"]
