A Water Tank Is Formed by Revolving the Curve $y = 2 x ^ { 4 }$

Multiple Choice

A water tank is formed by revolving the curve $y = 2 x ^ { 4 }$ about the $y$ -axis. Find the volume of water in the tank as a function of the water depth, $y$ .

A) $V ( y ) = \frac { \pi } { 2 \sqrt { 2 } } y ^ { 1 / 2 }$
B) $V ( y ) = \frac { 3 \pi } { 2 \sqrt { 2 } } y ^ { 3 / 2 }$
C) $V ( y ) = \frac { \pi } { 9 } y ^ { 9 }$
D) $V ( y ) = \frac { 2 \pi } { 3 \sqrt { 2 } } y ^ { 3 / 2 }$