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Cone development

Calculator of right circular cone / truncated right circular cone development

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

conus.jpg



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}

PLANETCALC, Cone development

Cone development

Second base radius (in case of frustum - truncated cone)
Digits after the decimal point: 2
Slant height
 
Lower arc radius
 
Upper arc radius
 
Central angle
 
Lower arc length
 
Upper arc length
 
Length of lower arc chord
 

Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Cone development

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