sphere(redirected from Volume of a sphere)
Also found in: Dictionary, Thesaurus, Medical, Legal.
sphere,in geometry, the three-dimensional analogue of a circlecircle,
closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
..... Click the link for more information. . The term is applied to the spherical surface, every point of which is the same distance (the radius) from a certain fixed point (the center), and also to the volume enclosed by such a surface. The curve formed by a plane cutting a sphere is a circle. If the plane goes through the center of the sphere, the circle is called a great circle of the sphere. It is the largest circle that can be drawn upon the sphere, and all great circles of the same or equal spheres are of equal size. The shortest distance between two points on a spherical surface, measured on the surface, is the distance along the great circle through those points. A plane cutting a sphere in a great circle divides the sphere into two equal segments called hemispheres. The diameter of a sphere is the diameter of one of its great circles. The formula for the area of the surface of a sphere is S=4πr2, and for the volume it is V= 4-3 πr3, where r is the radius of the sphere. Spherical geometry and spherical trigonometry are methods of determining magnitudes and figures on a spherical surface.
a closed surface all points of which are equally distant from a fixed point called the center of the sphere. A line segment joining the center and any of the points of a sphere is called the radius of the sphere. The term “radius” is also applied to the length of the segment. The area of a sphere is S = 4πR2, where R is the sphere’s radius.
The portion of space bounded by a sphere and containing its center is also called a sphere. The volume of such a portion of space is V = 4π/R3/3.
From the standpoint of analytic geometry, a sphere is a central quadric surface whose equation in rectangular coordinates has the form
(x – a)2 + (y – b)2 + (z – c)2 = R2
where a, b, and c are the coordinates of the center of the sphere.
the geometric solid generated by revolving a circle about its diameter. A sphere is the locus of points in space at a distance not greater than a specified distance R from a fixed point. The fixed point is called the center of the sphere, and R is known as the sphere’s radius. The volume of a sphere is V = 4πR3/3. The surface of a sphere is also called a sphere; its area is S = 4πR2.