Find the Area of the Surface Over the Given Region $\overrightarrow { \mathbf { r } } ( u , v ) = 6 u \cos v \hat { \mathbf { i } } + 6 u \sin v \hat { \mathbf { j } } + u \hat { \mathbf { k } }$

Multiple Choice

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone, $\overrightarrow { \mathbf { r } } ( u , v ) = 6 u \cos v \hat { \mathbf { i } } + 6 u \sin v \hat { \mathbf { j } } + u \hat { \mathbf { k } }$ where $0 \leq u \leq 2$ and $0 \leq v \leq 2 \pi$ .

A) $72 \sqrt { 37 } \pi$
B) $12 \sqrt { 37 } \pi$
C) $144 \sqrt { 37 } \pi$
D) $432 \sqrt { 37 } \pi$
E) $24 \sqrt { 37 } \pi$