Volume of a rotated ellipse by x=y

Question

I'm calculating a volume of a rotated ellipse by the line $x=y$ using Pappus Theorem, the ellipse has an equation of : $$(9x^2/16)+(36y^2/25)=1$$ Using Pappus Theorem, I can just plug in the length of centroid (d) to $x=y$ and area(A) to $$V = 2pi*dA$$ What I've been struggling for is to find the centroid, do I rotate the area under the line? if so, then how can I find the centroid for the area under the line? I've tried using the integration ones but I got $x ~ 0.9$ and that doesn't really makes sense.