# Mapping a cylinder onto a sphere

1. Feb 8, 2012

### c299792458

1. The problem statement, all variables and given/known data
How might I show that the map (in cylindrical polar coordinates) given by $f:(1,\phi,z)\to(\sqrt{1-z^2},\phi,z)$ does not change the area?

2. Relevant equations

3. The attempt at a solution
I can see this is like having a sphere in a cylinder and we shine "light" on the cylinder orthogonal to its axis inwards towards its axis so that the image falls on the unit sphere housed inside. A hint to the problem is given to be that the area of the spherical disc of spherical radius $r$ is $2\pi(1-\cos r)$.

2. Feb 9, 2012

### c299792458

Don't worry, I have solved it, thanks for reading though.