Let V Be the Volume of the Solid Generated by Revolving

Multiple Choice

Let V be the volume of the solid generated by revolving the region bounded above by $y = 2 x ^ { 2 }$ and bounded below the x-axis, $x \in [ 0 , \sqrt { 2 } ];$ about the y-axis. Then V is

A) $4 \pi$
B) $\frac { 128 \pi } { 3 }$
C) $\frac { 32 \pi } { 5 }$
D) $\frac { 8 \pi } { 3 }$
E) $\frac { 8 \pi } { 5 }$