# Homework Help: Volume of a 2-sphere on a 3-sphere

1. Apr 16, 2012

### XSerenity

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

On a 3-sphere of radius 1 defined using the coordinate system (r=1, χ,θ,$\phi$) where chi and theta run from 0 to π and $\phi$ runs from 0 to 2π. This coordinate system therefore has the metric

ds^2=dχ^2=[sin(χ)]^2*[dθ^2+[sin(θ)]^2*d$\phi$^2]

2. Relevant equations

How do I find the surface area of a 2-sphere defined by χ=χ0?

3. The attempt at a solution

3. I think wht I need to do is take the integral of ds over theta and phi. dχ=0, which leaves me with the following integral:

A=[sin(χ0)]^2 $\int \sqrt{dθ^2+[sin(θ)]^2*d\phi^2}$

I am not sure how to do this integral, as it does not even seem to be in the normal integral format. Am I going about this wrong? If not, how do I do this integral?