List of formulas in elementary geometry

This is a short list of some common mathematical shapes and figures and the formulas that describe them.

Two-dimensional shapes

:Sources:

Three-dimensional shapes

This is a list of volume formulas of basic shapes:

* Cone – $\frac\pi r^2 h$, where $r$ is the base's radius and $h$ is the cone's height;
* Cube – $a^3$, where $a$ is the side's length;
* Cuboid – $abc$, where $a$, $b$, and $c$ are the sides' length;
* Cylinder – $\pi r^2 h$, where $r$ is the base's radius and $h$ is the cylinder's height;
* Ellipsoid – $\frac\pi abc$, where $a$, $b$, and $c$ are the semi-major and semi-minor axes' length;
* Sphere – $\frac\pi r^3$, where $r$ is the radius;
* Parallelepiped – $abc\sqrt$, where $a$, $b$, and $c$ are the sides' length,$K = 1 + 2\cos(\alpha)\cos(\beta)\cos(\gamma) - \cos^2(\alpha) - \cos^2(\beta) - \cos^2(\gamma)$, and $\alpha$, $\beta$, and $\gamma$ are angles between the two sides;
* Prism – $Bh$, where $B$ is the base's area and $h$ is the prism's height;
* Pyramid – $\fracBh$, where $B$ is the base's area and $h$ is the pyramid's height;
* Tetrahedron – $a^3$, where $a$ is the side's length.

Sphere

The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables
*$r$ is the radius,
*$C = 2 \pi r$ is the circumference (the length of any one of its great circles),
*$S$ is the surface area,
*$V$ is the volume.

Surface area:

\begin
S
&= 4 \pi r^2 \\ .3ex&= \frac C^2 \\ .3ex&= \sqrt \\ .3ex\end

Volume:

\begin
V
&= \frac \pi r^3 \\ .3ex&= \frac C^3 \\ .3ex&= \frac S^ \\ .3ex\end

Radius:

\begin
r
&= \frac C \\ .3ex&= \sqrt \\ .3ex&= \sqrt \\ .3ex\end

Circumference:

\begin
C
&= 2 \pi r \\ .3ex&= \sqrt \\ .3ex&= \sqrt \\ .3ex\end

See also

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References

{{DEFAULTSORT:Formulas in elementary geometry
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Mathematics-related lists