Cone development

Calculator of right circular cone / truncated right circular cone development

Anton

Created: 2014-08-23 20:51:02, Last updated: 2020-12-11 13:47:47

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

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

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

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

Cone development

Second base radius (in case of frustum - truncated cone)
Digits after the decimal point: 2
Slant height

Central angle

Lower arc length

Upper arc length

Length of lower arc chord

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