+0  
 
0
82
1
avatar

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?

 Jan 19, 2021
 #1
avatar+9185 
0

area of sector / area of circle  =  100 / 360

 

Let  r  be the radius of the circle   so   the area of the circle  =  π r2

 

Substitute  250π  in for the area of the sector and substitute  π r2  in for the area of the circle.

 

250π  /  (π r2)   =   100 / 360

                                               Cancel out the  π's  in the first fraction

250 / r2   =   100 / 360

                                               Flip both sides of the equation

r2 / 250   =   360 / 100

                                               Multiply both sides of the equation by  250

r2   =   360 / 100 * 250

                                               Simplify the right side of the equation.

r2   =   900

                                               Take the positive square root of both sides.

r   =   30

 Jan 19, 2021

57 Online Users

avatar
avatar
avatar
avatar