$7\mathrm{.}82$ A circular plate with radius $r_1$ and unit thickness

has five holes drilled in it as shown in Figure P$7\mathrm{.}82.$ The

centers of the holes lie on an arc of radius $r_2.$ The spacing

between the centers is $60.$ Locate the centroid of the

volume of the plate if $r_1=0\mathrm{.}5m,r_2=0\mathrm{.}3m,$ and $r_3$

$=0\mathrm{.}1m.$

Figure P$7\mathrm{.}82$