The area of the surface $\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }$ , where $0 \leq u \leq 2 \pi$ and $0 \leq v \leq 2 \pi$ is

A) $12 \pi ^ { 2 }$
B)10 $\pi ^ { 2 }$
C)8 $\pi ^ { 2 }$
D)6 $\pi ^ { 2 }$
E)4 $\pi ^ { 2 }$

Question

The area of the surface

\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }

, where

0 \leq u \leq 2 \pi

and

0 \leq v \leq 2 \pi

is

A) $12 \pi ^ { 2 }$
B)10 $\pi ^ { 2 }$
C)8 $\pi ^ { 2 }$
D)6 $\pi ^ { 2 }$
E)4 $\pi ^ { 2 }$

Quizplus · Accepted Answer

The Answer of The area of the surface $\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }$ , where $0 \leq u \leq 2 \pi$ and $0 \leq v \leq 2 \pi$ is

A) $12 \pi ^ { 2 }$
B)10 $\pi ^ { 2 }$
C)8 $\pi ^ { 2 }$
D)6 $\pi ^ { 2 }$
E)4 $\pi ^ { 2 }$

The Area of the Surface r(u,v)=(2+cos⁡v)cos⁡ui+(2+cos⁡v)sin⁡uj+sin⁡vk\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }r(u,v)=(2+cosv)cosui+(2+cosv)sinuj+sinvk

The Area of the Surface $\mathbf { r } ( u , v ) = ( 2 + \cos v ) \cos u \mathbf { i } + ( 2 + \cos v ) \sin u \mathbf { j } + \sin v \mathbf { k }$