Sphere

Sphere

The geometric locus of points that are the same distance from a point called the centre of the sphere.
Sphere


A sphere may be obtained by rotating a circle about its diameter.

  • In the illustration below, the axis z contains a diameter of the circle.

Capture d’écran 2016-05-02 à 13.42.16

  • A sphere does not have a net.
  • The diameter of a sphere is the line segment that joins two points of a sphere and that passes through the centre of the sphere.
  • A great circle is the intersection of a sphere and a plane passing through the centre of a sphere.
  • A small circle is a section of a sphere formed by the intersection of a sphere and a plane that does not pass through the centre of the sphere.


Formulas

  • The area \(A\) of a sphere of radius \(r\) is : \(A=4\pi r^{2}\)
  • The volume \(V\) of a sphere of radius \(r\) is : \(V=\dfrac{4\pi r^{3}}{3}\)
  • The area of a sphere is equal to \(\dfrac{2}{3}\) of the total area of its circumscribed cylinder.
  • The area of a sphere is equal to \(\dfrac{4}{9}\) of the total area of its circumscribed right circular cone.
  • The volume of the space bounded by a sphere is equal to \(\dfrac{2}{3}\) of the volume of its circumscribed cylinder.
  • The volume of the space bounded by a sphere is equal to \(\dfrac{4}{9}\) of the volume of its circumscribed right circular cone.

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