Find the Area of the Surface $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k } ; 0 \leq u \leq 3,0 \leq v \leq 2 \pi$

Multiple Choice

Find the area of the surface.
The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k } ; 0 \leq u \leq 3,0 \leq v \leq 2 \pi$

A) $\frac { 5 \pi ( 37 \sqrt { 37 } - 1 ) } { 12 }$
B)
$\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 6 }$
C) $\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 12 }$
D) $\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 3 }$