A sphere has a surface area of \( 144\pi \) square centimeters. Find its radius.
["# Finding the Radius of a Sphere Given Its Surface Area", "Understanding how to calculate the radius of a sphere from its surface area is essential in geometry and real-world applications such as engineering, physics, and architecture. In this article, we’ll explore how to find the radius when the surface area of a sphere is known.", "## The Formula for a Sphere’s Surface Area", "A sphere is a perfectly symmetrical three-dimensional shape, and its surface area ( A ) is given by the mathematical formula:", "[\nA = 4\pi r^2\n]", "where:\n- ( A ) is the total surface area of the sphere,\n- ( r ) is the radius of the sphere, and\n- ( \pi ) approximately equals ( 3.14159 ).", "This formula arises from the geometry of a sphere and reflects how surface area scales with the square of the radius.", "## Given: Surface Area = ( 144\pi ) cm²", "We are told that the surface area of the sphere is ( 144\pi ) square centimeters. Substituting this into the surface area formula gives:", "[\n144\pi = 4\pi r^2\n]", "## Solving for the Radius", "To find ( r ), follow these steps:", "1. Divide both sides by ( \pi ) to eliminate ( \pi ) from the equation:", "[\n144 = 4r^2\n]", "2. Divide both sides by 4 to isolate ( r^2 ):", "[\nr^2 = \frac{144}{4} = 36\n]", "3. Take the square root of both sides to solve for ( r ):", "[\nr = \sqrt{36} = 6\n]", "Since radius is a positive quantity, we discard the negative root.", "## Conclusion: The Radius is 6 cm", "Therefore, the radius of the sphere with a surface area of ( 144\pi ) square centimeters is 6 centimeters.", "Knowing this relationship helps solve practical problems, from designing spherical containers to modeling planetary surfaces. Mastering the surface area formula and its inverse—finding radius from surface area—strengthens geometric problem-solving skills and supports applications in science and engineering.", "If you need to compute the radius of any sphere from its surface area, remember: solve ( r^2 = \frac{A}{4\pi} ), then take the positive square root. It’s a simple yet powerful geometry tool."]
