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?
+171 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 $30$.
+171 
her eis the image as well so you have an idea of what we are doing
