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

We know that whole circumference of a circle forms $2 \pi$ radian at the center. So $2 \pi$ radian is associated with whole area of the circle $\pi {r}^{2}$ ${\text{inch}}^{2}$. Where $r$ inch is the radius of the circle.Hence 4radian angle will be associated with sector of area $\frac{\pi {r}^{2}}{2 \pi} \cdot 4 = 2 {r}^{2}$
$2 {r}^{2} = 25$
$= r = \frac{5}{\sqrt{2}} = \frac{5}{2} \sqrt{2}$ inch