Quote:
Originally Posted by maurice
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.
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best part is if you turn it upside down, it does a great job of holding ice cream
anyway this description goes a long way in describing my page of math that I supplied. The page is a specific example where the base of the cone is 396, the top is 260 ( my cone was a truncated right angle cone) and the height of the cone was 228. Using pyrathos theorem I determined that the slant height was 237.
Where you see the number 396, 260, 228, 68, on my page you should be substituting your values for your truncated right circular conic section, and solve for the arc-angle in degrees, and the length of the two radii.