Question

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

Answer 1

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