A truncated cone - Math Central

HOME

Math Central

Quandaries & Queries

Question from Lucian:

I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet

Lucian,

Here is my diagram (not to scale) the dimensions are in millimeters., I hope it illustrates your situation.

cone

From the diagram x/152 = cos(20^o) and hence

x = 152 × cos(20^o) = 152 × 0.9397 = 143 mm.

Thus the inside radius of the base is

r = 725 + 143 = 868 mm.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.