# Sphere

## 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 $$A$$ 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.