from the symmetry of the region, is the area of the semicircle, is the distnace traveled by the centroid to generate the sphere so
Now for part a,
See if you can tackle part b.
Revolve the region about the x-axis to get and about the y-axis to get .
The region generates a cone of volume
when revolved about the x-axis, the area of the region is
, so .
A cone of volume is generated when the
region is revolved about the y-axis so .
The centroid is.........?