In spherical polar coordinates, the infinitesimal displacement ds is given by:
ds^2 = dr^2 + r^2 d\theta ^2 + r^2 \sin \left( \theta \right)^2 d\phi ^2
Can I find the volume of a sphere using ds?
The Attempt at a Solution
I know the spherical volume-element is given by [tex]dV = r^2 \sin \left( \theta \right)drd\theta d\phi[/tex].
I can always make a figure showing the geometry of spherical coordinates, but is there a general way of finding the volume from ds? Perhaps finding the area, and then the volume?