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

Multiple Choice

Find the exact area of the surface obtained by rotating the given curve about the x-axis. $x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$

A) $\frac { 24 \pi } { 5 }$
B) $\frac { 18 \pi } { 5 }$
C) $\frac { 12 \pi } { 5 }$
D) $\frac { 2 \pi } { 4 }$
E) None of these