A sphere has a surface area of \( 4\pi r^2 \). If the surface area is 144\(\pi\) square units, find the radius.

["### How to Find the Radius of a Sphere When Surface Area Is Given", "In geometry, understanding the relationship between a sphere’s surface area and its radius is essential for solving real-world problems in physics, engineering, and design. One of the fundamental formulas in spherical geometry is:", "[\n\ ext{Surface Area} = 4\pi r^2\n]", "This equation states that the surface area of a sphere depends entirely on the square of its radius (r), scaled by the constant (4\pi).", "#### Understanding the Problem", "Suppose you are given that the surface area of a sphere is (144\pi) square units. To find the radius, substitute this value into the surface area formula and solve for (r):", "[\n4\pi r^2 = 144\pi\n]", "#### Step-by-Step Solution", "1. Write the equation:\n Substitute the known surface area:\n [\n 4\pi r^2 = 144\pi\n ]", "2. Divide both sides by (4\pi):\n This isolates (r^2):\n [\n r^2 = \frac{144\pi}{4\pi} = \frac{144}{4} = 36\n ]", "3. Take the square root of both sides:\n Since radius is a positive measurement, we take only the positive root:\n [\n r = \sqrt{36} = 6\n ]", "#### Final Answer", "The radius of the sphere is 6 units.", "---", "### Why This Formula Matters", "Using the surface area formula (4\pi r^2) allows quick and accurate calculation of a sphere’s size without requiring complex measurements. This is particularly useful in fields such as architecture, medicine (e.g., calculating blood vessel surface area), or manufacturing spherical containers.", "---", "### Summary", "- Surface area of a sphere: (4\pi r^2)\n- Given surface area: (144\pi)\n- Solve: (4\pi r^2 = 144\pi) → (r^2 = 36) → (r = 6)\n- Radius is 6 units", "Knowing how to rearrange this formula helps solve a variety of geometric and applied science problems efficiently.", "---", "Keywords: sphere surface area formula, how to find radius from surface area, solve (4\pi r^2 = 144\pi), geometry practice problem, radius and surface area calculation, find r from surface area of sphere", "Meta Description: Learn how to calculate the radius of a sphere knowing its surface area using the formula (4\pi r^2). Step-by-step solution with example and key formulas. Perfect for geometry students and educators."]