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 surfaces 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
The surface area of a sphere is equal to the area of four great circles.