I'm working with surface integrals in spherical coordinates.
The equation of the surface of the sphere is simply r, yes? (not to be confused with the equation of the surface area of a sphere 4.pi.r^2)
When calculating the surface of a hemisphere, the equation of the curved surface of a hemisphere remains as r (not to be confused with the surface area of the hemisphere 2.pi.r^2)?
What about the closed base of the hemisphere, how do I explain, where that is, in spherical terms? Is it in the manner that we explain a circle in cartesian coordinates, ie r = x^2 + y^2 (not to be confused with the surface area of a circle pi.r^2)
I am really struggling with the understanding of the equation of the surface - I can carry out definite integrals quite happily for most shapes to find their volume/area, but I don't understand this surface equation?
Hope someone can help.