Area of a sector of a circle, whose angle is #(7pi)/6# is #175pi/12#. What is its radius?

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Answer 1 · 2016-10-07T12:39:29

Radius of circle is #5# feet

If the sector has an angle #theta# and radius #r#,

its area is #1/2r^2theta#

As such we have #1/2r^2theta=175pi/12#, where #r# is in feet.

or #1/2r^2xx(7pi)/6=175pi/12#

or #r^2=175pi/12xx(2xx6)/(7pi)#

= #r^2=175cancelpi/cancel12xxcancel(2xx6)/(7cancelpi)#

= #175/7=(5xx5xx7)/7=5xx5#

Hence radius of circle is #5# feet