Intersection of Sphere and Cone

Edit and compile if you like:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
\documentclass{article}
%
% File name: intersection-sphere-cone.tex
% Description: 
% A solid bounded by the following surfaces
% z = 0
% z = \sqrt{x^{2} + y^{2}}
% x^{2} + y^{2} + z^{2} = 1
% is generated. I.e., the intersection of half a sphere and a cone.
% 
% Date of creation: April, 23rd, 2022.
% Date of last modification: April, 23rd, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% 
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
\begin{document}
    %
    \tdplotsetmaincoords{60}{130}
    \begin{tikzpicture}[tdplot_main_coords,scale=1.75]
        \tikzmath{function f(\x) {return \x;};}
        \pgfmathsetmacro{\zini}{0.5*sqrt(2.0)}
        \pgfmathsetmacro{\step}{0.01}
        \pgfmathsetmacro{\zsig}{\zini+\step}
        \pgfmathsetmacro{\nextz}{\zini+0.5*\step}
        \pgfmathsetmacro{\sig}{2.0*\step}
        \pgfmathsetmacro{\tini}{0.5*pi}
        \pgfmathsetmacro{\tfin}{1.85*pi}
        \pgfmathsetmacro{\tend}{2.5*pi}
        %%% Coordinate axis
        \draw[thick,->] (0,0,0) -- (1.5,0,0) node [below left] {\footnotesize$x$};
        \draw[dashed,->] (0,0,0) -- (-1.5,0,0);
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX