is a solid bounded by closed surface every point of which is equidistant from a fixed point called the center.
Properties of a Sphere
Every section in the sphere made by a cutting plane is a circle. If the cutting plane passes through the center of the sphere, the section made is a great circle; otherwise the section is a small circle.
For a particular circle of a sphere, the axis is the diameter of the sphere perpendicular to the plane of the circle.
The ends of the axis of the circle of a sphere are called poles.
The nearer the circle to the center of the sphere, the greater is its area.
The largest circle in the sphere is the great circle.
The radius (diameter) of the great circle is the radius (diameter) of the sphere.
All great circles of a sphere are equal.
Every great circle divides the sphere into two equal parts called hemispheres.
The intersection of two spherical surfaces is a circle whose plane is perpendicular to the line joining the centers of the spheres and whose center is on that line. (See figure to the right.)
A plane perpendicular to a radius at its extremity is tangent to the sphere.
Formulas for a Sphere
Surface Area, A
The surface area of a sphere is equal to the area of four great circles.