View Single Post
 
Old 09-25-2009, 07:00 AM
maurice's Avatar
maurice maurice is offline
Member
 
Join Date: Jul 2007
Posts: 552
Total Downloaded: 219.9 KB
Might I try to help you sort out your wording ?
There is a thing called a right circular cone. Never not nothing else should it be called.
It's what most people think of in response to the word cone. So simple and obvious that I'll skip a precise definition of the animal unless you really want your ear bent.
Of the infinite variety of possible cones it is the only one of which the developed (unfolded) surface can be found by a simple numerical process.

Anyway waddever -

The developed surface of a right circular cone consits of a segment of a circular disc whose radius is equal to the slant height of the cone. (The slant height is the shortest distance down the outside of the cone.)
The angle, in degrees,included in the segment (not the angle in the bit that's discarded) and which lies at the centre of the disc, is found by dividing the radius of the base of the cone by the slant height and multiplying by 360.

That's all there is to it.

Quite obviously if the cone is truncated (chopped) by a plane normal (at right angles) to the axis of the cone then the developed shape needs to lose the chopped part and that's worked out in the same way. But it's easiest just to draw the arcs for the two slant heights at the same time.

You need to know how to do Development Drawing, either manually or in a CAD prog, or how to use an appropriatly competent computer prog if you want to develop the surface of any other sort of cone.

May you be happy with your cones.
Reply With Quote