The Region Under the Curve $y = 3 \sin ^ { 2 } x , 0 \leq x \leq \pi$

Multiple Choice

The region under the curve $y = 3 \sin ^ { 2 } x , 0 \leq x \leq \pi$ is rotated about the $x$ -axis. Find the volume of the resulting solid. Select the correct answer.

A) $\frac { 9 } { \pi ^ { 2 } }$
B) $\frac { 27 } { 8 } \pi ^ { 2 }$
C) $\frac { 3 } { \pi }$
D) $\frac { \pi ^ { 2 } } { 9 }$
E) $\frac { \pi } { 9 }$