$\text { A solid is generated by revolving the region bounded by } y = \sqrt { 100 - x ^ { 2 } } \text { and }$

Multiple Choice

$\text { A solid is generated by revolving the region bounded by } y = \sqrt { 100 - x ^ { 2 } } \text { and }$ $y = 0$ about the $y$ -axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-third of the volume is removed. Find the diameter of the hole. Round your answer to three decimal places.

A) $11.547$
B) $5.774$
C) $4.867$
D) $18.838$
E) $9.734$