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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The Answer of 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) $48 \pi \mathrm { m } ^ { 2 }$

The Surface of the Dome on a New Museum Is r=(u,v)=24sin⁡ucos⁡vi+24sin⁡usin⁡vj+24cos⁡uk\mathbf { r } = ( u , v ) = 24 \sin u \cos v \mathbf { i } + 24 \sin u \sin v \mathbf { j } + 24 \cos u \mathbf { k }r=(u,v)=24sinucosvi+24sinusinvj+24cosuk

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