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

3) given area of ellipse  \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 is \pi ab and that the volume generated when this area rotates through \pi about the x-axis is \frac{4}{3}\pi ab^2
use pappus' theorem to find the centroid.
for this i get the answer but not sure if its ok.

by pappus,with G y-coord of centroid

V=Axdistance travelled by G

 <br />
\frac{4}{3} \pi ab^2=(\pi ab)(\pi G)<br />

 <br />
G=\frac{4b}{3\pi} <br />

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