Spheres Topic Index | Geometry Index | Regents Exam Prep Center

Spheres are three-dimensional closed surfaces.

A sphere is a set of points in three-dimensional space equidistant from a point called the center.  The radius of the sphere is the distance from the center to the points on the sphere.

Spheres are not polyhedra.

Of all shapes, a sphere has the smallest surface area for its volume.

 The volume of a sphere is four-thirds times pi times the radius cubed. (Volume of a sphere:  r = radius)

Note:  A cross section of a geometric solid is the intersection of a plane and the solid.

 The surface area of a sphere is four times the area of the largest cross-sectional circle (called the great circle).

A great circle is the largest circle that can be drawn on a sphere.  Such a circle will be found when the cross-sectional plane passes through the center of the sphere.

 The equator is an examples of a great circle.  Meridians (passing through the North and South poles) are also great circles.      The shortest distance between two points on a sphere is along the arc of the great circle joining the points.The shortest distance between points on any surface is called a geodesic.  In a plane, a straight line is a geodesic.  On a sphere, a great circle is a geodesic.

What happens when planes
intersect with spheres?

 No, not that kind of plane!
 1.  The intersection of a plane and a sphere is a circle. 2.  If two planes are equidistant from the center of a sphere (and intersecting the sphere), the intersected circles are congruent.

A hemisphere is the half sphere formed by a plane intersecting the center of a sphere.

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