Surface area of a hemisphere w/ vector calculus

[simpleman008]

Homework Statement

I need help proving how you could use evaluation of the surface integral $$\oint\oint f(x,y,z)dS$$ to show that the surface area of the upper hemisphere of radius a is 2$$\pi$$ a².

So any ideas?

Homework Equations

The teacher mentioned that the divergence theorem would be the best way to go.

The Attempt at a Solution

Besides the hint from my teacher, i haven't gotten anywhere with the problem. It's one that has stumped my entire class. If anyone has any hints at all for where I can start with this problem, I would appreciate it greatly.

 

[lanedance]

so start with the divergence theorem... that tranforms a volume integral, to a surface integral over the bounding surface

so I would try setting up the volume integral first, then see if you can re-write the integrand as the divergence operator acting on a vector field... if you can do that ur pretty much there...

 

[lanedance]

sorry read the question incorrectly, i think you would actually do it backwards from what was described