Surface area of a hemisphere w/ vector calculus

  • #1

Homework Statement


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

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
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...
 
  • #3
lanedance
Homework Helper
3,304
2
sorry read the question incorrectly, i think you would actually do it backwards from what was described
 

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