Answer
$6.928\text{ cm}.$
Work Step by Step
Here, $r$ denotes the radius of the sector of the circle.
The Area of sector can be computed by the formula:
$A=\frac{\theta}{2}\cdot r^2$
where $\theta$ is the central angle measure in radians.
Hence here we have $6=\frac{\frac{1}{4}}{2}\cdot r^2\\6=\frac{1}{8}\cdot r^2\\6(8)=(8)\frac{1}{8}\cdot r^2\\48=r^2.$
Take the square root of both sides: $\sqrt{r^2}=\pm\sqrt{48}\\r=\pm\sqrt{48}\\r=\pm6.9282\approx6.928\text{ cm}$
Since $r$ is a radius, it can't be negative.
Thus, $r\approx6.928\text{ cm}.$
