Find the Area of the Surface of Revolution $\mathbf { r } ( u , v ) = 11 \sin u \cos v \mathbf { i } + 11 u \mathbf { j } + 11 \sin u \sin v \mathbf { k }$

Multiple Choice

Find the area of the surface of revolution $\mathbf { r } ( u , v ) = 11 \sin u \cos v \mathbf { i } + 11 u \mathbf { j } + 11 \sin u \sin v \mathbf { k }$ , where $0 \leq u \leq \pi$ and $0 \leq v \leq 2 \pi$ .

A) $121 \pi [ \sqrt { 2 } + \ln | \sqrt { 2 } - 1 | ]$
B) $22 \pi [ \sqrt { 2 } + \ln | \sqrt { 2 } + 1 | ]$
C) $242 \pi \left[ \sqrt { 2 } + \ln \left| \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 } \right| \right]$
D) $\pi [ \sqrt { 2 } - \ln | \sqrt { 2 } + 1 | ]$
E) $242 \pi \left[ \sqrt { 2 } + \ln \left| \frac { \sqrt { 2 } + 1 } { \sqrt { 2 } - 1 } \right| \right]$