A thin wire has the shape of the upper half of a circle with the center at the origin and a radius of $a$ in the $xy-$plane. Assume all distances are measured in meters. Given that the wire is made out of a material with density $(x,y,z)=k$ grams per meter $($for some positive parameter $k)$ find the mass and center of mass of the wire. Make sure to include units on your answers. $($Hint: Use symmetry as much as possible to simplify the calculations$).$