Properties Of Spheres

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What is a sphere? What are the properties of spheres? Information about radius, diameter and center of sphere.

Properties Of Spheres

sphere-1A circle is the set of all points in a plane that are at a given distance (the radius) from a fixed point (the centre) in the plane. A circular closed region is the union of a circle and its interior.

If we were to turn a circular closed region around a diameter as axis the 3 -dimensional figure made is a solid sphere.

If, in the diagram, the circular region of C(O,r) turns about the diameter [AB] the circle C(O,r) describes a sphere. Because every element of the circle is at a constant distance (r) from its centre (O), it follows that :

This given point is called the centre of the sphere, and the distance of each point of the sphere from its centre is called the radius of the sphere.

a sphere is the set of ail points at a given distance from a given point in space.

The symbol for a sphere with centre O and radius r is S(O,r). So the surface of a sphere is the sphere itself.

The union of a sphere with its interior is called a solid sphere. A line segment which passes through the centre of a sphere and has both endpoints on the sphere is called a diameter of the sphere.

The intersection of a plane with a sphere is a circle.

sphere-2

In the figure plane X intersects the sphere, S(O,R), but does not pass through the centre of the sphere, O. The intersection is the circle, C(N,r). We call such circles small circles on the sphere.

A small circle on a sphere is the intersection of a plane with the sphere and the plane does not pass through the centre of the sphere.

sphere-3

In this figure plane Y intersects the sphere, S(O,R), and passes through the centre of the sphere, O.

The intersection is the circle, C(O,R).

In this position the radius of the circle has its greatest length. This length is equal to the radius of the sphere. We call such circles great circles on the sphere.

A great circle on a sphere is the intersection of the sphere with any plane that passes through the centre of the sphere.





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