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Cone development

Calculator of right circular cone / truncated right circular cone development
Timur2014-08-23 20:51:02

Calculator computes parameters of right circular cone or truncated right circular cone development. The picture below illustrates the task.

We have radius of the lower base, radius of the upper base (in case of truncated cone), and cone height. We need to find length of lateral side (or slant height), radius of lower arc, radius of upper arc (again, in case of truncated cone), and common central angle.

Slant height can be found using Pythagoras.
$L = \sqrt{ (r_2 - r_1)^2 + H^2 }$,
for the full cone r1 is zero.

Radius of the upper arc can be found using triangles similarity.
$R_1=\frac{L*r_1}{r_2-r_1}$,
and for the full cone it is zero.

Radius of the lower arc thus
$R_2=L+R_1$,
and for the full cone it equals to L

And central angle
$\phi=360*\frac{r_2}{R_2}$

Cone development

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