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

question 101

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) \(24 \sqrt { 37 } \pi\)

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