Is Multiplying Divergence by Area Correct in Divergence Theorem Problems?

[joemama69]

Homework Statement

F = xi + yj + zk, s = x^2 + y^2 + z^2

Homework Equations

The Attempt at a Solution

div F = 1+1+1=3

area of sphere = 4pi

i can just multiply them to get 12pi as an answer right?

 

[dx]

No. You want the volume of the sphere, not the area.

 

[joemama69]

ooooops

V of sphere = 4/3 pi r^3 where r = 1, V = 4/3 pi

so i got 4pi

 

[dx]

Correct.