A sector of area 25 in^2 is formed by a central angle of 4 radians. Find the radius of the circle?

1 Answer
P dilip_k
Apr 18, 2018

We know that whole circumference of a circle forms #2pi# radian at the center. So #2pi# radian is associated with whole area of the circle #pir^2# #"inch"^2#. Where #r# inch is the radius of the circle.Hence 4radian angle will be associated with sector of area #(pir^2)/(2pi)*4=2r^2#

So by the problem

#2r^2=25#

#=r=5/sqrt2=5/2sqrt2# inch

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