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Use spherical coordinates. (a) Find the centroid of a solid homogeneous hemisphere of radius 1. (Assume...

Use spherical coordinates.

(a) Find the centroid of a solid homogeneous hemisphere of radius 1. (Assume the upper hemisphere of a sphere centered at the origin. Use the density function

ρ(x, y, z) = K.


(x, y, z) =


(b) Find the moment of inertia of the solid in part (a) about a diameter of its base.
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