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

Multiple Choice

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

A) $\frac { 28 \pi } { 7 }$
B) $\frac { 29 \pi } { 8 }$
C) $\frac { 28 \pi } { 9 }$
D) $\frac { 27 \pi } { 8 }$
E) $\frac { 29 \pi } { 9 }$