I have now sorted the first part of this question but cant get anywhere with part(b):

3) given area of ellipse is and that the volume generated when this area rotates through about the -axis is

use pappus' theorem to find the centroid.

for this i get the answer but not sure if its ok.

by pappus,with -coord of centroid

V=Axdistance travelled by G

so

I am unable to do the next part of the question:

b) find the first moment about Ox of that part of the area for which y>=0

i seem to need the perimeter of the ellipse here?

the answer in the book is