(2 points) Consider a solid upper hemisphere S with radius 9 centered at the origin. Find the centroid of S by following the steps below. Assume the density is constant 1.a. The mass of S is =1(,,)=m=S1d(x,y,z)=b. Let ()Q(z) be the disk that is the intersection of the hemisphere with the horizontal plane at height z.The radius of this disk is . So the area of the disk is .c. We can compute =(,,)=()(,)mz=Szd(x,y,z)=abQ(z)zd(x,y)dz where =a= and =b=.d. Hence =()1(,)=Area(())=mz=abzQ(z)1d(x,y)dz=abzArea(Q(z))dz=ab =dz=e. Using the symmetry of the hemisphere, the center of gravity is (0,0,)(0,0,z) where ==z=mzm=.