Find the Area of the Surface Generated by Revolving $x = 3 \cos ^ { 3 } \theta , y = 3 \sin ^ { 3 } \theta , 0 \leq \theta \leq \pi / 2$

Multiple Choice

Find the area of the surface generated by revolving the curve about the given axis. $x = 3 \cos ^ { 3 } \theta , y = 3 \sin ^ { 3 } \theta , 0 \leq \theta \leq \pi / 2$
(i) $x$ -axis;(ii) $y$ -axis

A) (i) $\frac { 27 } { 5 } \pi$ ; (ii) $\frac { 27 } { 5 } \pi$
B) (i) $\frac { 54 } { 5 } \pi$ ; (ii) $\frac { 54 } { 5 } \pi$
C) (i) $\frac { 27 } { 10 } \pi$ ; (ii) $\frac { 27 } { 5 } \pi$
D) (i) $\frac { 54 } { 5 } \pi$ ; (ii) $\frac { 27 } { 5 } \pi$
E) (i) $\frac { 54 } { 5 } \pi$ ; (ii) $\frac { 108 } { 5 } \pi$