Surface Area of a Sphere

The Greek mathematician Archimedes discovered that the surface area of a sphere is the same as the lateral surface area of a cylinder having the same radius as the sphere and a height the length of the diameter of the sphere.

The lateral surface area of the cylinder is 2πrh where h = 2r.

 Lateral Surface Area of the Cylinder = 2πr(2r) = 4πr².

Therefore, the Surface Area of a Sphere with radius r equals 4πr².