# Patch of a surface in spherical coordinates?

## Homework Statement

I am currently trying to prove:

S = ∫∫a2sinΦdΦdθ

Here is my work (note that in my work I use dS instead of S, this is an accident):

I end up with:

S = ∫∫a*da2sinΦdΦdθ

Where da is the infinitesimal thickness of the surface.

Why am I getting the wrong answer?

Dick
Homework Helper

## Homework Statement

I am currently trying to prove:

S = ∫∫a2sinΦdΦdθ

Here is my work (note that in my work I use dS instead of S, this is an accident):

I end up with:

S = ∫∫a*da2sinΦdΦdθ

Where da is the infinitesimal thickness of the surface.

Why am I getting the wrong answer?
You haven't computed S. You've computed the volume V=S*da. To get S, divide by the da.

You haven't computed S. You've computed the volume V=S*da. To get S, divide by the da.
I thought that if the volumetric shell thickness approaches zero you end up with the surface area?

Dick