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Sphere
r
= radius |
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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.
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The
volume of a
sphere is four-thirds times pi times the radius cubed.
(Volume of a sphere: r = radius)
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Note: A cross section
of a geometric solid is the intersection of a plane and the solid.
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The
surface area
of a sphere is four times the area of the
largest cross-sectional circle (called the great circle).
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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.
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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. |
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What happens when planes
intersect with spheres?
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No, not that kind of plane! |
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1. The intersection of a plane and a sphere
is a circle.
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2. If two planes are equidistant from the center
of a sphere (and intersecting the sphere),
the intersected circles
are congruent.
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A
hemisphere is the half sphere formed by a plane intersecting the
center of a sphere.
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