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A sector of a circle has a central angle of 100. If the area of the sector is 250\pi, what is the radius of the circle?

 Jun 25, 2021
 #1
avatar+151 
+2

the formula for finding the area of a circle sector is:

 

$ \mathcal{A}= \frac{\theta }{360}  \times \pi r^2 $ where $\mathcal{A}=$Area    ;   $\theta=$given angle  ;  $r=$radius  

 

we are given the value of area and theta. so lets substitute that in:

 

$ 250 \pi= \frac{100}{360}  \times \pi r^2  $

 

you can cancel the $\pi$s, so you get 

 

$ 250= \frac{100}{360} \times  r^2 \ \ \overset{ simplify }{===== \Rightarrow} \ \ \ 250 = \frac{5}{18} \times  r^2    $

 

$  5r^2=4500  $

 

$ r^2=900  $

 

$ r=\pm \sqrt{900}  $

 

        $\Updownarrow  $

 

$ r=30$  and  $r=$-30 

 

 

only the positive one is valid, thus, the radius of that circle is $30$. 
 

 Jun 25, 2021
 #2
avatar+151 
+1

her eis the image as well so you have an idea of what we are doing

UsernameTooShort  Jun 25, 2021

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