Radius (Geometry)
From Halbeeg, the open encyclopedia · Af-Soomaali
107 languages
A radius is a straight line connecting the center of a circle or sphere to any point on its circumference or surface. The term also refers to the length of this line. Thus radius can denote either a geometric line or a numerical measurement.
All radii of a circle are equal in length. This is the defining property of a circle: all points at a fixed distance from the center constitute the circle. If the center and the radius are known, the circle is completely determined.
Relationship to diameter
The diameter is a line passing through the center with endpoints on the circumference. The diameter equals twice the radius: d = 2r. Conversely, the radius is half the diameter.
Measurement formulas
The circumference of a circle is C = 2πr. The area is A = πr². For a sphere: the volume is V = (4/3)πr³, and the surface area is S = 4πr². The constant π is approximately 3.14159.
Other uses
Radius appears in other geometric contexts. For example, a regular polygon has a circumradius (the distance from the center to a vertex) and an apothem (the distance from the center to the midpoint of a side). In the polar coordinate system, r represents the distance from a point to the origin.