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: $A = \frac{c^{2}}{π} = \frac{2 c^{2}}{τ}$

Using the diameter: $A = π d^{2} = \frac{τ d^{2}}{2}$

Using the radius: $A = 2 τ r^{2} = 4 π r^{2}$

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

Circumference

Using the surface area: $c = \sqrt{π A} = \sqrt{\frac{τ A}{2}}$

Using the diameter: $c = π d = \frac{τ d}{2}$

Using the radius: $c = τ r = 2 π r$

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

Diameter

Using the surface area: $d = \sqrt{\frac{A}{π}} = \sqrt{\frac{2 A}{τ}}$

Using the circumference: $d = \frac{c}{π} = \frac{2 c}{τ}$

Using the radius: $d = 2 r$

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

Radius

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

Using the circumference: $r = \frac{c}{τ} = \frac{c}{2 π}$

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

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

Volume

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

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

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

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

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

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