The Area of the Surface Generated by Revolving the Curve $x ( t ) = 3 t ^ { 2 } , y = 2 t ^ { 3 }$

Multiple Choice

The area of the surface generated by revolving the curve $x ( t ) = 3 t ^ { 2 } , y = 2 t ^ { 3 }$ with $t \in [ 0,1 ]$ about the y-axis is

A) $\frac { 24 \pi ( 1 + \sqrt { 2 } ) } { 7 }$
B) $\frac { 24 \pi ( \sqrt { 2 } - 1 ) } { 3 }$
C) $\frac { 24 \pi ( \sqrt { 2 } - 1 ) } { 5 }$
D) $\frac { 24 \pi ( 1 + \sqrt { 2 } ) } { 5 }$
E) $\frac { 24 \pi ( 1 + \sqrt { 2 } ) } { 3 }$