Find a Such That the Volume Inside the Hemisphere $z = \sqrt { 100 - x ^ { 2 } - y ^ { 2 } } \text { and outside }$

Multiple Choice

Find a such that the volume inside the hemisphere $z = \sqrt { 100 - x ^ { 2 } - y ^ { 2 } } \text { and outside }$ the cylinder $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ is one-half the volume of the hemisphere. Round your answer to four decimal places.

A) $a = 12.1662$
B) $a = 9.0831$
C) $a = 33.0831$
D) $a = 26.0831$
E) $a = 6.0831$