How Does Radian Measure Relate to Sector Area in a Circle?

[resresd]

in a circle with perimeter of 20cm a sector has radius r, angle θ radians and area Acm^2
prove that A= 25-(r-5)^2

A=1/2 r^2 θ
c=2Πr

the only thing that I can think to do is c=2Πr therefore 20=2Πr
10=Πr r=10/Π
so then A=1/2 r^2 θ
=1/2 (10/Π)^2 θ
= θ (100/2Π^2)

 

[sutupidmath]

Why don't you post the entire question again, and in a neat way, it will make life easier for everybody here, and surely you will get more responses!

EDIT: you can just edit the first post, and delete the others, or ask a PF to delete the others.

 

[resresd]

i can't seem to get the 2s to show up superscript...is there a particular way?

 

[sutupidmath]

you might want to use LATEX if you are familiar with that at all? or you can just do it
r^2, and we will know that r is raised to the power of 2.

 

[resresd]

thanks, i hope this is better

 

[HallsofIvy]

Honestly, it looks to me like that statement is not true and so cannot be proved. For one thing, it does not involve "$\theta$" and that can't be right.

 

[Jamil (2nd)]

I believe that the statement should have been like this:

A sector of a circle has a perimeter of 20cm and a area of "A" and the circle has a radius of "r". Prove that "A = 25-(r-5)(r-5)"

Now with simple methods, show that the arc of sector is (20-2r). Find the angle of sector in terms of "r". Then substitute the angle to the area of sector and it is proved easily.

 

[HallsofIvy]

If you are not given the angle, how could you possibly prove that the length of the arc of the sector is 20- 2r? The length obviously depends on $\theta$.

 

[Jamil (2nd)]

Indeed it does, but the perimeter also allows to find the Arc length, since the perimeter is the addition of the three sides (Arc length and two radii):

(Length of Arc) + (2 * radius) = Perimeter of Sector

or, Length of Arc = Perimeter of Sector - (2 * radius)

or, Length of Arc = 20 - 2r

 

[HallsofIvy]

OH! The original post read "a circle with perimeter of 20cm" and when you changed it to "A sector of a circle has a perimeter of 20cm " I was still thinking about the circled and just thought about the length of the arc.