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# Help geometry

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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
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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
+152
+1

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