The Area of the Surface $\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }$

Multiple Choice

The area of the surface $\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }$ , where $0 \leq u \leq 2 \pi$ and $0 \leq v \leq 2 \pi$ is

A) $12 \pi ^ { 2 }$
B) 10 $\pi ^ { 2 }$
C) 8 $\pi ^ { 2 }$
D) 6 $\pi ^ { 2 }$
E) 4 $\pi ^ { 2 }$