Sector of a circle

troublemaker676

Junior Member
Joined
Sep 1, 2005
Messages
84
I have to find the area of the sector of a circle. I don't know how to draw it up so i will give you guys the measurements. The radius of the big circle is 56, the radius of the small circle is 21. They want the area(exact, not approxiamate) of the 10 degree region between the small circle and the big circle. I hope this is clear. I have no idea how to do it. Thanks for any help in advance. :D
 
A "sector" is a pie-wedge-shaped portion of a circle. No other circle is involved in finding the area of a sector of some given circle.

How are the two different circles in your picture related? What do you mean by "10° region"? What do you mean by "between the small circle and the big circle?" What are the instructions of the exercise? Are you supposed to find the difference in areas between a sector with r = 56 and another sector with r = 21, given that both sectors have central angles of 10°?

Also, you say you "have no idea how to do it." Have sectors and arcs not been covered in class, so you don't have any of the formulas and need a link to an online lesson?

Please reply with clarification. Thank you.

Eliz.
 
Hello, troublemaker676!

]I have to find the area of the sector of a circle.
The radius of the big circle is 56, the radius of the small circle is 21.
They want the area(exact, not approxiamate) of the 10 degree region between the small circle and the big circle.
Code:
                                         D
                                          *
                           B       *       * 
                            *               *
                      *      *              *
                *             *              * 
          *  10°              *              *
    *-------------------------*--------------*
    O           21            A              C 
    | - - - - - - - - - 56 - - - - - - - - - |

Since the central angle, \(\displaystyle 10^o\), is \(\displaystyle \;\frac{10}{360}\,=\,\frac{1}{36}\;\) of the full circle,

. . the large sector \(\displaystyle OCD\) has area: \(\displaystyle \L\frac{1}{36}\,\times\,\pi\cdot56^2\:=\:\frac{784}{9}\pi\) units\(\displaystyle ^2\)

. . the smaller sector\(\displaystyle OAB\) has area: \(\displaystyle \L\frac{1}{36}\,\times\,\pi\cdot21^2\:=\:\frac{49}{4}\pi\) units\(\displaystyle ^2\)


Therefore, the area between the circles is: \(\displaystyle \L\;\frac{784}{9}\pi\,-\,\frac{49}{4}\pi\;=\;\frac{2695}{36}\pi\) units\(\displaystyle ^2\)
 
Geesh, why try and show this poor fellow "areas of sectors"
when he still is unable to do a simple circle area? (see his other post).
 
I can find the area of a circle, i don't think you guys understand my question. I really need to be able to draw it out, can any of you instruct me on how to do this?
 
I assume ( as did Soroban) that you have two concentric circles of radii 21 and 56.
A slightly different way:
The area of the big circle is pi*56²
The area of the small circle is pi*21²
The area you want is 10/360 of the difference. That will give the same answer as Sorobans.
 
Thank you guys very much, i know the directions were hard to understand, and I think the correct term might have been segment not sector (sorry stapel). :D
 
troublemaker676 said:
I think the correct term might have been segment not sector
If you are referring to the area between an arc and a chord of a circle, the arc and the chord sharing endpoints, then yes, the term would be "segment".

If, on the other hand, you are referring to a pie-wedge-shaped portion of a circle, then no, the correct term is "sector".

Please clarify, as the answer will be different if you really meant "segment".

Thank you.

Eliz.
 
Yes, the correct term would be segment not sector. Sorry about the confusion the only instructions were "SA=", nothing else, and i mistaked the "s" as standing for sector not segment and i realized that was incorrect.
 
troublemaker676 said:
Yes, the correct term would be segment not sector.
So the picture Soroban drew is not correct, nor (likely) are the numerical answers provided...?

Since a "segment" involves one circle with an arc and a chord, how do the two circles you mentioned relate to each other?

Eliz.
 
So both Soroban and I are misreading it and you mean
Code:
       / @
      /   @
     /     @
    /* AREA @
   /  *      @
  /    *      @  
 / 10°  *      @
O--------*------@--
<-- 21 ->|      |
<------ 56 ---->|
The *s are a chord of the small circle 
The @s are a chord of the large circle
If that's what you mean
http://www.1728.com/circsect.htm
may help but it does use sine from trig.
-------------------
Gene
 
That is correct, but the way soroban did it made perfect sense and i think it is right. (I DO know that it is not an annulus). So is soroban's answer right? If not what is?
 
troublemaker676 said:
That is correct, but the way soroban did it made perfect sense and i think it is right.
Soroban was assuming you were referring to sectors, not to segments. Since the problem has changed, the answer likely has changed as well.

troublemaker676 said:
So is soroban's answer right? If not what is?
Have you noticed how we keep having to ask you please to explain what you mean? If you don't know what the question is asking, how do you expect us to know? And how are we to divine the answer?

I'm sorry, but I left my crystal ball in my other pants.... :roll:

Eliz.
 
I have already said stapel that the question is asking for the SEGMENT, I have already explained this in my other posts, and the picture that Gene has illustrated is CORRECT . :x
 
If you check out the site I mentioned you will see that what you are after is NOT a segment. If my picture is correct is a trapazoid and not properly any named part of a circle. Staple has the weakness of using terms correctly. I just let my imagination run wild :evil:
--------------------------
Gene
 
Your question could simply be worded this way:
You have a big washer radius 56, with radius of circular hole = 21.
What's the area of the metal? What's 10% of that?

IT IS AN ANNULUS :twisted:
 
Dude, chill out! She is just asking you to be as specific as possible. There is no point in throwing a tantrum. She is only trying to help the other tutors help YOU! Please be more polite to our tutors seeing as they are here to help us. It isn't as if they get paid to do this, and since you aren't posting the FULL problem, they cannot fully help you. Please just calm down. No one on this board holds a grudge and I am positive that Stapel will forgive you in a heartbeat. I bet she's already forgotten!! :wink: Just be nice to everyone and please be more precise. Thank you and PLEASE have a nice day.
 
I have already stated the problem, this is the only information I have, again I have explained this in my other posts, THAT IS THE FULL PROBLEM!!!

"The radius of the big circle is 56, the radius of the small circle is 21. They want the area(exact, not approxiamate) of the 10 degree region between the small circle and the big circle."

"Sorry about the confusion the only instructions were "SA=", nothing else." :evil:
 
troublemaker676 said:
... this is the only information I have..."The radius of the big circle is 56, the radius of the small circle is 21."....the only instructions were "SA=", nothing else.
So there was no picture of the circles, so we have no way of knowing if they share a center, or overlap, or are utterly unrelated? And there is no way of knowing what "A" or "S" or "SA" might have to do with either of the circles?

And there is no explanation of how "ten degrees" (which measures an angle) somehow relates to an area or a distance (which could plausibly be a measure of something "between the circles")?

And there is no explanation of how "segments" might relate to this exercise, as indeed they are nowhere mentioned within "the full problem" that you quoted?

I don't see how yelling at us will clarify the exercise. You would probably have better luck asking the instructor for clarification, such as a graphic which illustrates whatever the exercise is asking for. :roll:

Eliz.
 
Top