Find coordinates of center of mass of a quarter sector of a uniform disk of radius $r$ placed in the first quadrant of a Cartesian coordinate system with centre at origin.

From the result obtained for sector of circular plate distance $OC$ of the center of mass form the center is

$OC=\frac{2r\sin (\pi /4)}{3\pi /4}=\frac{4\sqrt{2}r}{3\pi }$

Coordinates of the center of mass $\left(x_c,y_c\right)$ are $\left(\frac{4r}{3\mathrm{\pi }},\frac{4r}{3\mathrm{\pi }}\right)$