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

question 41

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) \(\frac { \pi ( 37 \sqrt { 37 } - 1 ) } { 3 }\)

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