Editing Cone (section)

====Surface area====
The [[lateral surface]] area of a right circular cone is <math>LSA = \pi r \ell</math> where <math>r</math> is the radius of the circle at the bottom of the cone and <math>\ell</math> is the slant height of the cone.<ref name=":0" />  The surface area of the bottom circle of a cone is the same as for any circle, <math>\pi r^2</math>.  Thus, the total surface area of a right circular cone can be expressed as each of the following:

*Radius and height
::<math>\pi r^2+\pi r \sqrt{r^2+h^2}</math>
:(the area of the base plus the area of the lateral surface; the term <math>\sqrt{r^2+h^2}</math> is the slant height)

::<math>\pi r \left(r + \sqrt{r^2+h^2}\right)</math>
:where <math>r</math> is the radius and <math>h</math> is the height.

[[File:Cone_surface_area.svg|thumb|Total surface area of a right circular cone, given radius 𝑟 and slant height ℓ]]
*Radius and slant height
::<math>\pi r^2+\pi r \ell</math>

::<math>\pi r(r+\ell)</math>
:where <math>r</math> is the radius and <math>\ell</math> is the slant height.

*Circumference and slant height
::<math>\frac {c^2} {4 \pi} + \frac {c\ell} 2</math>

::<math>\left(\frac c 2\right)\left(\frac c {2\pi} + \ell\right)</math>
:where <math>c</math> is the circumference and <math>\ell</math> is the slant height.

*Apex angle and height
::<math>\pi h^2 \tan \frac{\theta}{2} \left(\tan \frac{\theta}{2} + \sec \frac{\theta}{2}\right)</math>
::<math>-\frac{\pi h^2 \sin \frac{\theta}{2}}{\sin \frac{\theta}{2}-1}</math>
:where <math> \theta </math> is the apex angle and <math>h</math> is the height.