Two Concentric Sectors

A

Aza

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Hey people. Just one before the new years starts here. Been having trouble with the concentric sectors in 2 circles problem. Every time I do it on graphing paper it doesn't work out for me, 80 degrees just seems too much, I am not sure. Please tell me I am wrong because I don't think this matches up.
.Concentric sectors.JPGConcentric sectors 2.JPG
 
The first line in the answer to part (i) is wrong. You say that "arc length" is 2 and θ (angle AOB) is 1.4 but how did you get these values?

You may need to re-read your notes regarding what the terms "arc length" and "r" actually refer to.

Hint: there are a few more steps to answer part (i) of this question than you might think. Think about how many arcs there are in the diagram and what the arc length equation says about each of them.
 
NOTE I think the "2cm" label between D and A refers only to the length of DA rather than the full length of OA

( Such a mis-reading might have led you to the values that you wrote in part i )
 
Aza said:
Hey people. Just one before the new years starts here. Been having trouble with the concentric sectors in 2 circles problem. Every time I do it on graphing paper it doesn't work out for me, 80 degrees just seems too much, I am not sure. Please tell me I am wrong because I don't think this matches up.
.View attachment 15776View attachment 15777
Click to expand...
Aza, you need THIS PAGE Cubist is correct the arc lengths are \(\displaystyle L=2~\&~2.8\),
If we say \(\displaystyle \theta\) is the measure of the angle then \(\displaystyle (OD)\cdot\theta=2~\&~[(OD+2)]\cdot\theta=2.8\)
Now solve for \(\displaystyle \theta~.\)
 
I'm sorry I am really having trouble with this question, I don't understand how to rearrange this, I'm lost as to how to get theta without having a radius..
 
Aza said:
I'm sorry I am really having trouble with this question, I don't understand how to rearrange this, I'm lost as to how to get theta without having a radius..
Click to expand...

I'll add some further explanation to pka's post...

Consider "arc DC" first. The radius is not known, so call it "OD". Using the arc formula you obtain... (OD) × θ=2
Now consider "arc AB". The radius is "OD"+2, since the radius is 2 greater than the previous arc's radius. The arc formula now gives... (OD+2) × θ=2.8

You now have two equations and two unknowns. You can use simultaneous equation methods to find θ.
(OD) × θ=2
(OD+2) × θ=2.8 -> (OD)×θ + 2×θ=2.8

Can you finish this off to find length OD?
 
Aza said:
I'm sorry I am really having trouble with this question, I don't understand how to rearrange this, I'm lost as to how to get theta without having a radius..
Click to expand...
Aza, did you study THIS PAGE ?
If you did and still have questions then you need to have help from a live tutor.
You need to have a sit-down with a tutor and come to an understanding about the components in this question.
 
Cubist and pka, thank you kindly for all your help, I think I have solved it.Sector working.jpgcapture 2.JPG
 
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