We haven't discussed volume integrals yet in our vector analysis class, which means maybe I was really expected to intuit that I need to get 5 surfaces and then add them? But isn't it the problem states that I have to find

... which indicates a surface integral? By the way thanks for sticking with me on this.. Yeah we have already discussed divergence, gradient, and curl

I know that the divergence of A is nabla dot A but I don't know what it has to do with volume, I always thought the value of divergence just meant that the particles are moving away from or towards a certain point. I do know how nabla dot A is calculated and why that became 0 + 1 + 0 = 1. Also I know how you got the volume of the quarter cylinder it was (pi*(r^2)*h)/4. But why would multiplying the volume by the divergence give you the value of the surface integral? and why is everything above in our previous posts wrong and this one correct?