Made it too easy for you eh? ;)
Based on your sketch, should there not be 10 layers? And out of curiosity, what are you making?
If the top of each layer intersects the (hemi-) sphere, the top plank has zero radius. It could just be a vertical spike or something.
Making the intercept at the centre of each layer, as for the planks in the 2-dimensional version, would give you a non-infinitesimal top layer.
@useless started
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Made it too easy for you eh? ;)
Based on your sketch, should there not be 10 layers? And out of curiosity, what are you making?