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.
Find the surface area of a sphere with radius 5 inches.
S. A. = 4π(5)2 = 100π inches2 ≈ 314.16 inches2