A sector of a circle has a central angle of 210 degrees and an area of 21 π / 4. Find the radius of the circle.

Question

A sector of a circle has a central angle of 210 degrees and an area of   21  π      /    4. Find the radius of the circle.

uglasiteveh · Accepted Answer

formula for area of a sector of a circle :   A  =  1      /    2  (      r    2    )  θ  A  =  21  π      /    4  θ  =  210 degrees(must convert to radians using conversion factor   π      /    180  )  =  7  π      /    6      r          2        =  A      /    (  1      /    2  ∗  θ  )  =  (  21  π      /    4  )      /    (  1      /    2  ∗  7  π      /    6  )  =  (  21  π      /    4  )  (  12      /    7  π  )  =  9 (remember just like the other problem flip the fraction to divide by it)  r  =      9    =  3

Baylee Atkinson · Accepted Answer

area of sector of a circle  =  1      /    2      r          2        θbut given that   A  =            21      π        θ       a  n  d     θ  =  210 degrees  ∴      r          2        =            21      π        θ    ×      2    210        r          2        =  9r=3 is the answer.

A sector of a circle has a central angle of 210 degrees and an area of 21pi /4. Find the radius of the circle.

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