Find the flux $\overrightarrow { \mathrm { F } } \text { of through } S , \iint _ { S } \overrightarrow { \mathrm { F } } \cdot \overrightarrow { \mathrm { N } } d S \text {, where } \overrightarrow { \mathrm { N }}$ is the upward unit normal vector to S.
$\overrightarrow { \mathrm { F } } ( x , y , z ) = x \hat { \mathbf { i } } + y \hat { \mathbf { j } } + z \hat { \mathbf { k } }$
$S : z = 64 - x ^ { 2 } - y ^ { 2 } , z \geq 0$
A) $4,301 \pi$
B) $6,144 \pi$
C) $7,987 \pi$
D) $3072 \pi$
E) $1843.2 \pi$

Question

Find the flux $\overrightarrow { \mathrm { F } } \text { of through } S , \iint _ { S } \overrightarrow { \mathrm { F } } \cdot \overrightarrow { \mathrm { N } } d S \text {, where } \overrightarrow { \mathrm { N }}$ is the upward unit normal  vector to S. 
$\overrightarrow { \mathrm { F } } ( x , y , z ) = x \hat { \mathbf { i } } + y \hat { \mathbf { j } } + z \hat { \mathbf { k } }$
$S : z = 64 - x ^ { 2 } - y ^ { 2 } , z \geq 0$
A) $4,301 \pi$
B) $6,144 \pi$
C) $7,987 \pi$
D) $3072 \pi$
E) $1843.2 \pi$

Quizplus · Accepted Answer

The Answer of Find the flux $\overrightarrow { \mathrm { F } } \text { of through } S , \iint _ { S } \overrightarrow { \mathrm { F } } \cdot \overrightarrow { \mathrm { N } } d S \text {, where } \overrightarrow { \mathrm { N }}$ is the upward unit normal  vector to S. 
$\overrightarrow { \mathrm { F } } ( x , y , z ) = x \hat { \mathbf { i } } + y \hat { \mathbf { j } } + z \hat { \mathbf { k } }$
$S : z = 64 - x ^ { 2 } - y ^ { 2 } , z \geq 0$
A) $4,301 \pi$
B) $6,144 \pi$
C) $7,987 \pi$
D) $3072 \pi$
E) $1843.2 \pi$

Find the Flux Is the Upward Unit Normal Vector to S