The problem is following: Assume that we have a area, lets call it $K$ that is limited by a cone $z=-\sqrt{x^2+y^2}$ and by a sphere $x^2+y^2+z^2 = 16$
Now, in this problem they want me to describe the area K using inequlities. More specifically in spherical coordinates
My attempt:
Spherical coordinates are given by:
$\left\{x = r \sin\theta \cos\phi \\y=r \sin\theta \sin\phi \\z=r \cos\theta\right\}$
where $0 \leq \theta \leq \pi, \space 0\leq \phi \leq 2\pi$
So this gives us: $x^2+y^2 = r^2 \sin\theta$
After that I'm basically a bit lost, the only restriction we have, for the variables $x$, $y$ and $z$ are that they range between $\pm4$.