- #1
Karnage1993
- 133
- 1
Homework Statement
Let ##S## be the portion of the sphere ##x^2 + y^2 + z^2 = 9##, where ##1 \le x^2 + y^2 \le 4## and ##z \ge 0##. Give a parametrization of ##S## using polar coordinates.
Homework Equations
The Attempt at a Solution
##1 \le r \le 2 \\
0 \le \theta \le 2\pi \\
0 \le \phi \le \pi / 2##
We are currently doing 2-dim surfaces in ##\mathbb{R}^3## so I can't do a parametrization of the form ##\Phi (r, \theta, \phi)## so instead, I let ##\theta = 4\phi## so that
##\Phi (r, \phi) = (r\cos(4\phi)\sin(\phi), r\sin(4\phi)\sin(\phi), r\cos(\phi))##.
But when I put it into Mathematica, the graph looks nothing like what it should be. Have I made the correct parametrization? It looks like some sort of spiral shape. What I am thinking it SHOULD look like is the area between the sphere with radius 2 and the unit sphere.