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