Surface area and volume of a cubic section using spherical coordinates:

Question

anonymous · Answer

Do you have a specific problem in mind?   What is it they you need to understand?  You haven't provided enough detail.

anonymous · Answer

The question is to find the surface area of the spherical section and the enclosed volume of:
$$0\le R \le2, 0 \le \theta \le 90^o, 30^o \le \phi \le 90^o$$
and then draw it the section

anonymous · Answer

Is the integral for the surface area:  $$\int\limits_{0}^{90^o} \int\limits_{30^o}^{90^o} R^2\sin \theta d \theta $$

anonymous · Answer

except you are missing $$d \phi $$

anonymous · Answer

Ok thanks what about the volume integral how would that look?

anonymous · Answer

try this wiki page for the details http://en.wikipedia.org/wiki/Spherical_coordinate_system The volume element and surface element is also listed under "Integration and differentiation in spherical coordinates"

anonymous · Answer

Thats great thanks for the help

anonymous · Answer

I suggest you review this http://tutorial.math.lamar.edu/Classes/CalcIII/TISphericalCoords.aspx this is a great site for calcIII stuff. Suggest referencing this when on shaky ground

anonymous · Answer

I use it frequently, one can't remember everything especially when I don't use stuff much like spherical coordinates.  Cheers!

anonymous · Answer

Very true thanks again