
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 28th, 2018, 01:50 AM  #1 
Newbie Joined: Jun 2018 From: Jordan Posts: 14 Thanks: 0  Making a cone out of a circle's sector
Hey. Say that we have a circle sector with sectoral angle $\displaystyle \theta$ and radius $\displaystyle r$, then we join the radii of the sector together, forming the cone in a way that would make the cone's base circumference equal to the length of the sector's arc length. Slant height of the cone would be $\displaystyle r$. The question is, would the angle of the cone's vertex (if we take its face at some point which is a triangle) be the same as $\displaystyle \theta$? credits to some guy from stack exchange ^ Last edited by skipjack; July 29th, 2018 at 12:38 AM. 
July 28th, 2018, 11:29 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 
Why are you showing the diagram on left?

July 28th, 2018, 11:41 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,122 Thanks: 1102 
Your notation is a bit confusing. Let your sector have radius $\ell$ and angle $\theta$ The base circumference of the cone will be $\ell \theta$ and the base radius will be $r = \dfrac{\ell \theta}{2\pi}$ The cone vertex angle will be $\phi = \arcsin\left(\dfrac{r}{\ell}\right) = \arcsin\left(\dfrac{\theta}{2\pi}\right)$ 
July 29th, 2018, 07:44 AM  #4 
Newbie Joined: Jun 2018 From: Jordan Posts: 14 Thanks: 0 
Aha. So it's a new angle at last? Alright thanks, this guy @ stack exchange confused me. @Denis: the picture isn't mine, I got it from some question @ stack exchange. I think he did that to elaborate and relate things more (theta, the slant height and radius) 

Tags 
circle, cone, making, sector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Making a Cone Tent  Cyryn  Art  4  December 15th, 2017 12:48 AM 
circle inscribed inside parabolic sector  galactus  Calculus  5  September 3rd, 2015 01:45 PM 
Converting degrees to radians and finding an area of a sector of a circle  matheus  Trigonometry  1  March 31st, 2015 06:46 AM 
Area of a Sector of a Circle  Julie  Algebra  2  May 18th, 2009 11:41 AM 
sector and segment of a circle  sheen_daphne  Algebra  3  December 10th, 2008 07:09 AM 