Sphere

A sphere (also spelled kubad) is a three-dimensional geometric object. It is defined as the set of all points on its surface that lie at equal distance from a single point called the center. This equal distance is called the radius.

The sphere is the most symmetrical three-dimensional shape. It has no edges, no straight lines, and its surface is uniform on all sides. For this reason it is one of the most-used shapes in mathematics, physics, and engineering.

Definition and parts

The center is the point at the middle of the sphere. The radius (r) is the distance between the center and any point on the surface. The diameter is twice the radius, and is the longest line passing through the sphere and its center. Any line passing through the sphere and its center divides it into two equal parts called hemispheres.

Mathematical formulas

The surface area of a sphere is calculated as 4πr². The volume of the interior of a sphere is calculated as (4/3)πr³. Both formulas depend only on the radius, showing that any two spheres are identical if their radii are equal.

Distinction between surface and volume

Some languages distinguish between the surface of a sphere alone and the solid object within it. In English, 'sphere' often refers to the surface, while 'ball' is used for the solid object. In Somali, the word 'kubad' can refer to both, with the meaning distinguished by context.

Natural occurrence and application

The spherical shape occurs naturally when a compressive force draws matter together uniformly, as with large stars and planets, and also with water droplets shaped by surface tension. Celestial bodies do not form perfect spheres, as rotation causes their equatorial regions to bulge.