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January 11th, 2012, 06:32 AM  #1 
Newbie Joined: Jan 2012 Posts: 3 Thanks: 0  Relationship between angle in a cone and circle?
I want to know if there is a relationship between a the angle of the sector of a circle which can be turned into a cone, and the angle inside the cone.

January 15th, 2012, 08:00 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond  Re: Relation ship between angle in a cone and circle? 
January 17th, 2012, 12:01 AM  #3 
Newbie Joined: Jan 2012 Posts: 3 Thanks: 0  Re: Relation ship between angle in a cone and circle?
Thanks a lot. The help's much appreciated . I tried finding out experimentally using google sketchup, 3d modelling software. Could'nt find any proper relation between the angles that way though .

January 17th, 2012, 12:07 AM  #4 
Newbie Joined: Jan 2012 Posts: 3 Thanks: 0  Re: Relation ship between angle in a cone and circle?
Oh, and by the way, are there any sources explaining how the relation is derived 
January 17th, 2012, 12:26 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond  Re: Relationship between angle in a cone and circle?
Here is my derivation: Let be the old radius and be the new radius. Then the circumference of the cone is , where is the angle contained in the sector. so The sine of the angle in question is so the angle is 
January 24th, 2012, 02:06 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Relationship between angle in a cone and circle? Hello, rozze! And here is my derivation of the formula . . . Quote:
We have a circle of radius The diagram shows that a minor sector (less than a semicircle) is removed.[color=beige] .[/color][color=red]**[/color] The central angle of the remaining major sector is Code: ..*.*.*.. *:::::::::::* * \:::::::/ * * R\:::::/R * \:::/ * \:/ * * * * * * @ * * * * * * * * * The circumference of the major sector is The major sector is formed into a cone. Its slant height is Let be its base radius. Let be half its vertex angle. Code: * /\ / A\ /  \ R /  \ R /  \ /  \ /  \ *    +    * r r The circumference of the base is [color=beige]. . [/color] ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ [color=red]**[/color] Of course, the portion removed need not be a minor sector.  

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