The Un-Uniform Sphere

Geometry Level pending

Given a nonuniform sphere of radius 1 with 65.62% of the original volume removed as a spherical plug tangent to point "H" on the lower surface the resultant centroid shifted upward from 1/2 to 5/8 of the diameter. How much of the original volume can be removed maintaining the new centroid location if the spherical plug removed is now tangent to point "O" at the center of the sphere? Provide your answer to 2 decimal places in percent.

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