Find the Flux of the Vector Field F Across the Surface

question 46

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } = \mathrm { x } ^ { 5 } \mathrm { yi } - \mathrm { zk }$ ; $\mathrm { S }$ is portion of the cone $\mathrm { z } = 4 \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } }$ between $\mathrm { z } = 0$ and $\mathrm { z } = 3$ ; direction is outward

• A) \(- \frac { 27 } { 8 } \pi\)
• B) \(- \frac { 9 } { 16 }\)
• C) \(\frac { 9 } { 8 } \pi\)
• D) \(- \frac { 9 } { 8 } \pi\)