How to find the raius of a circle

a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

Question:-

A sector of a circle has an area of 90 cm²and a central angle of 0.2radians .Find it's radius.


Answer:-

Area of sector = 90 cm²

Central angle = 0.2 radians

We need to convert this central angle to degrees

degrees=radians x 180/π

degrees=0.2 x 180/3.142

=11.5 degrees

                 11.5
Area of sector= -------- x area of the circle
                 360

    
             11.5
        90= ------ x πr2 
              360
The above step is having area of a circle formula
Let's find the radius (r) from the above equation

             90 x 360
            ---------- = r2
              11.5 π

          
             90 x 360
            ---------- = r2
             11.5x3.142


              896.8= r2


               r = √896.8 = 29.9

      So radius is approximately equal to 30 is the answer
We can use this in circumference of a circle formula to get the
circumference of the circle,similar ,if know the area of sector
for earth we can even find the radius of earth