Sphere
The geometric locus of points that are the same distance from a point called the centre of the 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.
- 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 [latex]A[/latex] of a sphere of radius [latex]r[/latex] is : [latex]A=4\pi r^{2}[/latex]
- The volume [latex]V[/latex] of a sphere of radius [latex]r[/latex] is : [latex]V=\dfrac{4\pi r^{3}}{3}[/latex]
- The area of a sphere is equal to [latex]\dfrac{2}{3}[/latex] of the total area of its circumscribed cylinder.
- The area of a sphere is equal to [latex]\dfrac{4}{9}[/latex] of the total area of its circumscribed right circular cone.
- The volume of the space bounded by a sphere is equal to [latex]\dfrac{2}{3}[/latex] of the volume of its circumscribed cylinder.
- The volume of the space bounded by a sphere is equal to [latex]\dfrac{4}{9}[/latex] of the volume of its circumscribed right circular cone.