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January 28th, 2015, 04:25 PM  #1  
Newbie Joined: Jan 2015 From: WA Posts: 3 Thanks: 0  reposted: sewing conundrum concerning cones
Accidentally posted this in high school geometry first. Yeah, I think this is way out of their league. So after some research (i.e., googling "what is topology") I figured it's better suited for ths forum instead. Quote:
 
January 29th, 2015, 06:06 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
This isn't really topology, but I'll answer it here rather than shuffle it around further. Let's say the angle of the sector you cut out is $\alpha.$ Then the circumference of the new inner circle is the circumference of the original inner circle (let's call it C) times $1\frac{\alpha}{2\pi}$. Setting that equal to 40 we get $C=\frac{40}{1\frac{\alpha}{2\pi}}$ or $r=\frac{40}{2\pi\alpha}.$ Now the radius of the large circle is 24 more, or $\frac{40}{2\pi\alpha}+24.$ This makes the (original) outer circumference $\frac{80\pi}{2\pi\alpha}+48\pi.$ You'll then cut out the same angle from it, making the new outer circumference $$ \left(\frac{80\pi}{2\pi\alpha}+48\pi\right)\left(1\frac{\alpha}{2\pi}\right). $$ I'm not sure how you want to measure the wedge width. The 'missing' outer circumference is $$ \alpha\left(\frac{40}{2\pi\alpha}+24\right) $$ and the 'missing' inner circumference is $$ \frac{40\alpha}{2\pi\alpha}. $$ If you prefer to measure in degrees, replace $\pi$ with $180^\circ.$ 

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cones, conundrum, reposted, sewing 
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