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

Area of a sector of a circle, whose angle is (7pi)/6(7pi)/6 is 175pi/12175pi/12. What is its radius?