Let \(R>0\) and \(H>0\), and let \(\mathcal{W}\) be the upper half of the ellipsoid \(x^{2}+y^{2}+(R z / H)^{2}=R^{2}\), where \(z \geq 0\) (Figure 16). Find the centroid of \(\mathcal{W}\) and show that it depends on the height \(H\) but not on the radius \(R\).


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