Evaluate $\iint _ { S } f ( x , y , z ) d S$

question 13

Multiple Choice

Evaluate $\iint _ { S } f ( x , y , z ) d S$
$f ( x , y , z ) = z ; S$ is the part of the torus with vector representation
$$\mathbf { r } ( u , v ) = ( 5 + 3 \cos v ) \cos u \mathbf { i } + ( 5 + 3 \cos v ) \sin \imath \mathbf { j } + 3 \sin v \mathbf { k } , 0 \leq u \leq 2 \pi , 0 \leq v \leq \frac { \pi } { 2 } .$$
Select the correct answer.

• A) 0
• B) \(117 \pi\)
• C) 117
• D) \(27 \pi\)

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