Formation of a Cone
Date: 03/16/2003 at 21:44:42 From: Star Subject: Formation of a cone Why is a cone formed when a sector is removed from a circle and the edges of the remaining segment joined? Does it have to do with the change in proportions?
Date: 03/17/2003 at 10:13:30 From: Doctor Marshall Subject: Re: Formation of a cone This is exactly why! When you take a sector from a circle you aren't changing the radius of the shape (it's no longer a circle), but you are reducing the partial circumference (i.e., the arc length, or curved perimeter). Next the partial circumference is squeezed back into a new smaller circle, but the radius is still the same as it was, and the center of the (old) circle is still the _same_ _distance_ from every point in the new circumference. So we have a (new) circle with (new) radius r, and some point that is equidistant from every point in that circle, namely R units away from each point, and R is much bigger than r. Such a point does not exist in 2-D. We must send our center point out into 3-D, as the apex of the cone. The old radius now becomes the slant height of the cone. Does this make sense? Hope this helps. Write back if you have any more questions. - Doctor Marshall, The Math Forum http://mathforum.org/dr.math/
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