The Surface of the Dome on a New Museum Is $\mathbf { r } = ( u , v ) = 24 \sin u \cos v \mathbf { i } + 24 \sin u \sin v \mathbf { j } + 24 \cos u \mathbf { k }$

question 39

Multiple Choice

The surface of the dome on a new museum is given by $\mathbf { r } = ( u , v ) = 24 \sin u \cos v \mathbf { i } + 24 \sin u \sin v \mathbf { j } + 24 \cos u \mathbf { k }$ , where $0 \leq u \leq \frac { \pi } { 3 }$ and $0 \leq v \leq 2 \pi$ and $\mathbf { r }$ is in meters. Find the surface area of the dome.

• A) \(288 \pi \mathrm { m } ^ { 2 }\)
• B) \(1152 \pi \mathrm { m } ^ { 2 }\)
• C) \(24 \pi \mathrm { m } ^ { 2 }\)
• D) \(576 \pi \mathrm { m } ^ { 2 }\)
• E) \(48 \pi \mathrm { m } ^ { 2 }\)

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