Sphere

A Sphere

A sphere is a round, three-dimensional shape. All points on the edge of the sphere are at the same distance from the center. The distance from the center is called the radius of the sphere. A real-world sphere is called a globe if it is large (such as the Earth), and as a ball if it is small, like an association football.

Common things that have the shape of a sphere are basketballs, superballs, and playground balls. The Earth and the Sun are nearly spherical, meaning sphere-shaped.

A sphere is the three-dimensional analog of a circle.

Calculating measures of a sphere

Surface area

Using the circumference: $A={\frac {c^{2}}{\pi }}={\frac {2c^{2}}{\tau }}$

Using the diameter: $A=\pi d^{2}={\frac {\tau d^{2}}{2}}$

Using the radius: $A=2\tau r^{2}=4\pi r^{2}$

Using the volume: $A={\sqrt[{3}]{3\tau V^{2}}}={\sqrt[{3}]{6\pi V^{2}}}$

Circumference

Using the surface area: $c={\sqrt {\pi A}}={\sqrt {\frac {\tau A}{2}}}$

Using the diameter: $c=\pi d={\frac {\tau d}{2}}$

Using the radius: $c=\tau r=2\pi r$

Using the volume: $c={\sqrt[{3}]{6\pi ^{2}V}}={\sqrt[{3}]{\frac {3\tau ^{2}V}{2}}}$

Diameter

Using the surface area: $d={\sqrt {\frac {A}{\pi }}}={\sqrt {\frac {2A}{\tau }}}$

Using the circumference: $d={\frac {c}{\pi }}={\frac {2c}{\tau }}$

Using the radius: $d=2r$

Using the volume: $d={\sqrt[{3}]{\frac {6V}{\pi }}}={\sqrt[{3}]{\frac {12V}{\tau }}}$

Radius

Using the surface area: $r={\sqrt {\frac {A}{2\tau }}}={\sqrt {\frac {A}{4\pi }}}$

Using the circumference: $r={\frac {c}{\tau }}={\frac {c}{2\pi }}$

Using the diameter: $r={\frac {d}{2}}$

Using the volume: $r={\sqrt[{3}]{\frac {3V}{2\tau }}}={\sqrt[{3}]{\frac {3V}{4\pi }}}$

Volume

Using the surface area: $V={\sqrt {\frac {A^{3}}{18\tau }}}={\sqrt {\frac {A^{3}}{36\pi }}}$

Using the circumference: $V={\frac {c^{3}}{6\pi ^{2}}}={\frac {2c^{3}}{3\tau ^{2}}}$

Using the diameter: $V={\frac {\pi d^{3}}{6}}={\frac {\tau d^{3}}{12}}$

Using the radius: $V={\frac {2\tau r^{3}}{3}}={\frac {4\pi r^{3}}{3}}$

Equation of a sphere

In Cartesian coordinates, the equation for a sphere with a center at $(x_{0},y_{0},z_{0})$ is as follows:

$(x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}$

where $r$ is the radius of the sphere.

Related pages

• Circle
• Pi
• Tau