Evaluate $\iint _ { S } f ( x , y , z ) d S$.
$f ( x , y , z ) = 2 x + 2 y + 5 z ; S$ is the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes $z = 1$ and $z = 2$.
A) $70 \pi \sqrt { 2 }$
B) $70 \sqrt { 2 }$
C) $\frac { 70 } { 3 } \pi \sqrt { 2 }$
D) 0

Question

Quizplus · Accepted Answer

The surface integral over the cone can be evaluated using cylindrical coordinates. The integral of $f(x, y, z)$ over the surface $S$ involves integrating over the region defined by the cone between $z = 1$ and $z = 2$. The correct evaluation leads to $\frac { 70 } { 3 } \pi \sqrt { 2 }$.

Evaluate ∬Sf(x,y,z)dS\iint _ { S } f ( x , y , z ) d S∬S​f(x,y,z)dS

Evaluate $\iint _ { S } f ( x , y , z ) d S$