A typical giant panda has a mass of $110kg$. A very rough model of a panda (such as the one shown below) would be to approximate it as two spheres, one resting on top of the other.

The radius of the lower (body) sphere is $R$, and the radius of the upper (head) sphere is $R/2$. The contribution of all other parts of the panda is assumed to be negligible for purposes of computing the center of mass. By observation of the symmetry of the model, the horizontal location of the center of mass of the panda lies upon the vertical line running through the center of the panda.

Assuming constant density throughout the panda, and treating the bottom of the lower sphere as the $y=0$ point, where is the vertical center of mass of the panda?

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