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.

A Sphere

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: ${\displaystyle A={\frac {c^{2}}{\pi }}={\frac {2c^{2}}{\tau }}}$

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

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

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

Circumference

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

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

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

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

Diameter

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

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

Using the radius: ${\displaystyle d=2r}$

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

Radius

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

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

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

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

Volume

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

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

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

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

Equation of a sphere

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

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

where ${\displaystyle r}$ is the radius of the sphere.

Related pages

• Circle
• Pi
• Tau