Small challenge

[Csaba Tizedes]

(06-09-2017 01:14 PM)Vtile Wrote:  I'll throw in another small and easy challenge ( especially since I give a picture. ). You are making cones out of cardboard, what are the measures of the cut out piece when it is then bend to cone and the dimensions for the cone are as follows.

angle Alpha: 30 deg.
R: 30
Hx: 5

From these equations (\(\beta\) in radian):
\(R_2 · \beta=2 · r · \pi\), and

\((R_2+s) · \beta=2 · R · \pi\)

we get:
\(R_2=\frac{\frac{h_x}{cos \alpha}}{\frac{R}{R-h_x}-1}\), and

\(\beta=\frac{2 · (R-h_x) · \pi}{R_2}\)

All the other simplification is your task


Csaba