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

Multiple Choice

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

A) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 6 }$
B) $\frac { 5 \pi ( 17 \sqrt { 17 } - 1 ) } { 12 }$
C) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 12 }$
D) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 3 }$