Geometric Properties of a Sphere
In three-dimensional Euclidean geometry, a sphere is the set of all points in three-dimensional space that are located at a fixed distance r (the radius) from a given point (the center).
Volume Formula
The volume of a sphere represents the capacity of space enclosed inside it. It was first derived by Archimedes of Syracuse using the lever balance principle:
V = 4/3 × π × r³
Where V is volume, r is radius, and π is mathematical constant approximately 3.14159.
Surface Area Formula
The surface area of a sphere equals four times the area of its great circle (the circle formed by cutting the sphere directly through its center):
A = 4 × π × r²