# Finding volumes from infinitesimal displacements

1. May 4, 2008

### Niles

1. The problem statement, all variables and given/known data
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?

3. The attempt at a solution
I know the spherical volume-element is given by $$dV = r^2 \sin \left( \theta \right)drd\theta d\phi$$.

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?

Last edited: May 4, 2008
2. May 4, 2008

### Niles

No hints at all?

I thought of ds^3, but ds is a vector, so that wont work.