- #1

- 71

- 0

## Homework Statement

How might I show that the map (in cylindrical polar coordinates) given by [itex]f:(1,\phi,z)\to(\sqrt{1-z^2},\phi,z)[/itex] does not change the area?

## Homework Equations

## 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 [itex]r[/itex] is [itex]2\pi(1-\cos r)[/itex].