An Un-Uniform Sphere

Geometry Level pending

Given a nonuniform sphere of radius 1 with 27.72% of the original volume removed as a spherical plug tangent to the center of the sphere at point "O" the resultant centroid shifted upward from \(\frac12\) to \(\frac58\) of the diameter. What is the percentage left of the original volume while maintaining the new centroid position when the spherical plug is tangent at point "H" on the lower surface? Provide your answer to 2 decimal places in percent.

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