A sphere has a surface area of \(144\pi\) square centimeters. What is its radius? (Use \(\pi \approx 3.14\))

["How to Find the Radius of a Sphere Given Its Surface Area – A Step-by-Step Guide", "Understanding the geometry of a sphere is essential in both mathematics and real-world applications. One of the key properties of a sphere is its surface area, which plays an important role in fields like physics, engineering, architecture, and design. If you’re ever asked to find the radius of a sphere when given its surface area, this guide will walk you through the formula and calculation — using the fact that a sphere’s surface area (A = 144\pi) cm², and approximating (\pi \approx 3.14).", "---", "### What Is the Surface Area of a Sphere?", "The surface area (A) of a sphere with radius (r) is calculated using the formula:", "[\nA = 4\pi r^2\n]", "This formula comes from integrating the surface area of infinitesimally small circular strips that make up the sphere’s outer layer. Knowing this formula allows you to solve for the radius when the surface area is known — exactly what we’ll do.", "---", "### Step-by-Step: Find the Radius", "Given:", "[\nA = 144\pi \ \ ext{cm}^2 \quad \ ext{and} \quad \pi \approx 3.14\n]", "Substitute into the surface area formula:", "[\n144\pi = 4\pi r^2\n]", "First, divide both sides of the equation by (\pi) (since (\pi <br/>\neq 0)):", "[\n144 = 4r^2\n]", "Next, divide both sides by 4:", "[\nr^2 = \frac{144}{4} = 36\n]", "Now take the positive square root (radius cannot be negative):", "[\nr = \sqrt{36} = 6\n]", "---", "### Verification", "Plug the radius back into the surface area formula to confirm:", "[\nA = 4\pi (6)^2 = 4\pi \ imes 36 = 144\pi \ \ ext{cm}^2\n]", "This matches the given surface area, confirming our result.", "---", "### Conclusion", "If a sphere has a surface area of (144\pi) square centimeters, its radius is:", "[\n\boxed{6 \ \ ext{cm}}\n]", "This straightforward calculation demonstrates how fundamental geometric formulas empower precise measurements — a valuable skill in science, engineering, and daily life. Next time you encounter a sphere’s surface area, recall this clear procedure to find its radius accurately!"]