Process$-$Oriented Problem $05\mathrm{.}003-3-$D Centroid

You are working on a project that uses a machine component that has the shape seen in the image below. This particular project requires knowledge of the centroid of the machine component with which you are working It is known that the machine component is made out of a homogeneous material with the dimensions as shown. There is a vertical cylindrical cutout in the base of the machine component. Your task is to determine the coordinates of the centroid of this machine component

where $a=0\mathrm{.}6m,b=0\mathrm{.}2m,c=0\mathrm{.}2m,d=0\mathrm{.}5m,e=0\mathrm{.}4m,f=0\mathrm{.}8m,g=1\mathrm{.}6m,h=0\mathrm{.}2m,r=0\mathrm{.}4m,$ and $i=2\mathrm{.}2m$

Process$-$Oriented Problem $05\mathrm{.}003.$f $-3-$D Centroid

Determine the total volume of the machine component. $($Round the final answer to three decimal places.$)$

The total volume of the machine component is $m^3$