How to draw a 3D sphere and a 3D cone for Spherical coordinates

Question

I'm trying to replicate this figure:

Right know, I have this code:

\begin{figure}[H]
    \centering
    \begin{tikzpicture}[yzx, scale = 0.9]
        \draw[->] (0,0,0) -- (5.5,0,0) node(x)[left]{$x$};
        \draw[->] (0,0,0) -- (0,5,0) node(y)[right]{$y$};
        \draw[->] (0,0,0) -- (0,0,4) node(z)[right]{$z$};
    \def\px{4}; \def\py{4}; \def\pz{4};
    \coordinate (o) at (0,0,0);
    \coordinate (p) at (\px,\py,\pz);
    \coordinate (pxy) at (\px,\py,0);


    % Spherical coordinates
    \begin{scope}[canvas is xy plane at z=0]
        \draw[->, cadmiumorange] (2,0) arc(0:45:2) node[pos = 0.5, below]{$\phi$};

        \draw[dotted, cadmiumorange] (o) -- (pxy);
    \end{scope}

    \draw[cadmiumorange] (o) -- (p) node[above left, pos = 0.5]{$r$};

    \draw[dotted] (pxy) -- (p) node[pos = 0.5, right]{$z$};

    \begin{scope}[canvas is zy plane at x=0]
        \draw[->, cadmiumorange] (1,0) arc(0:45:1) node[pos = 0.5, above]{$\theta$};
    \end{scope}


    % x-y-z coordinates
    \draw[bleudefrance] (o) -- (\px,0,0) node[above, pos = 0.5, sloped]{$x$};

    \draw[bleudefrance] (\px,0,0) -- (pxy) node[pos = 0.5, below]{$y$};


    % Point
    \filldraw (p) circle(3pt) 
    node[above right]{$P(r, \theta, \phi)$} 
    node[below right]{$P(x,y,z)$};
\end{tikzpicture}
\caption{Coordenadas cartesianas y esf\'ericas.}
\label{c2:definiciones:esfericasB}

\end{figure}

that produces

That's all I'm able to draw by my own. I don't know how to draw this "solids" sphere and cone. The text in the first figure is in spanish but it's not needed in the answer.

The ideal asnswer to this question would be an answer like the answer of this question: How to draw the solids to refer to cylindricals coordinates. This answer is (relatively) easy to understand and modify.

I also have this in my code:

\documentclass[11pt, oneside]{book}
\usepackage{pgfplots}
\pgfplotsset{compat = newest}
\usepackage{tikz-3dplot}
\usepackage{tikz}
    \usetikzlibrary{snakes, calc, quotes, babel, hobby, trees, arrows, patterns, patterns.meta, calligraphy, backgrounds, chains, shapes.geometric, shapes, angles, 3d, fillbetween,
    decorations, decorations.pathreplacing, 
    decorations.pathmorphing, decorations.markings, decorations.text}
\tikzstyle{yzx} = [
    x={(-.385cm, -.385cm)},
    y={(1cm, 0cm)},
    z={(0cm, 1cm)},
]
\tikzset{zxplane/.style={canvas is zx plane at y=#1,very thin}}
\tikzset{yxplane/.style={canvas is yx plane at z=#1,very thin}}


\usepackage{tkz-euclide}
\tikzset{every picture/.style = {line width = 1pt, > = Triangle},
    %
    %
    %
    set arrow inside/.code = {\pgfqkeys{/tikz/arrow inside}{#1}},
    set arrow inside={end/.initial = >, opt/.initial =},
    /pgf/decoration/Mark/.style = {
        mark/.expanded = at position #1 with {
            \noexpand\arrow[\pgfkeysvalueof{/tikz/arrow inside/opt}]{\pgfkeysvalueof{/tikz/arrow inside/end}}
        }
    },
    arrow inside/.style 2 args = {
        line width = 2pt,
        set arrow inside = {#1},
        postaction = {
            decorate, decoration={
                markings, Mark/.list = {#2}
            }
        }
    },
}


\usepackage{physics} 
\usepackage[italic = true]{derivative}
\usepackage[scr = rsfso]{mathalfa}
\usepackage{mathtools}
\usepackage{amssymb}
\definecolor{cadmiumorange}{rgb}{0.93, 0.53, 0.18}

Thanks for reading and keep helping!

Answer 1

You can draw something like your picture essentially using the canvas is... options from 3d library. For example:

\tikzset
{
   xz/.style={canvas is xz plane at y=0},
   xz rotated/.style={rotate around z=\mytheta,xz},
}

Here I'm defining two styles. The first one draw in the xz plane (if you choose a different y then draws in a parallel plane at distance y). The second draws in another plane, obtained rotating the xy plane around the z-axis \mytheta degrees (defined to be 60).

Using these new planes you only need to draw a few straight lines and a couple of arcs, all of them related to the angles \mytheta and \myphi.

A complete example (well... I left the labels for you) could be:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{3d} % for 'canvas is...' options
\tikzset
{% styles
   axis/.style={thick,-latex},
   yz/.style={canvas is yz plane at x=0},
   xz/.style={canvas is xz plane at y=0},
   xz rotated/.style={rotate around z=\mytheta,xz},
   xy elevated/.style={canvas is xy plane at z={\myradius*cos(\myphi)},scale={sin(\myphi)}},
   sphere/.style={shading=ball,fill opacity=0.3},
   plane/.style={fill=teal,fill opacity=0.3},
   cone/.style={fill=yellow,fill opacity=0.3},
   vector/.style={very thick,-stealth},
   point/.style={shading=ball,ball color=red}
}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,
                    x={(-0.4cm,-0.4cm)}, y={(1cm,0)},z={(0,1cm)}]
% dimensions
\def\myradius{5}
\def\mytheta{60}
\def\myphi{30}
% axes
\draw[axis] (0,0,0) -- (1.3\myradius,0,0) node[below] {$x$};
\draw[axis] (0,0,0) -- (0,1.3\myradius,0) node[right] {$y$};
\draw[axis] (0,0,0) -- (0,0,1.3*\myradius) node[above] {$z$};
% sphere
\draw[sphere] (0,\myradius,0) {[yz] arc (0:90:\myradius)} {[xz rotated] arc (90:0:\myradius)} arc (\mytheta:90:\myradius);
% plane
\draw[plane,xz rotated] (0,\myradius) arc (90:0:\myradius) -| cycle;
% cone
\draw[cone] {[xy elevated] (\myradius,0) arc (0:\mytheta:\myradius) coordinate (P)} -- (0,0,0) -- cycle;
% other arcs
\draw (\mytheta:\myradius) arc (\mytheta:0:\myradius) {[xz] arc (0:90:\myradius)};
\draw[-latex] (1,0,0) arc (0:\mytheta:1) node[midway,below] {$\theta$};
\draw[xz rotated,-latex] (0,2) arc (90:90-\myphi:2) node[midway,above] {$\varphi$};
% vectors
\draw[xz rotated ,vector] (P) --++ (90-\myphi:1.5) node[above] {$\hat{r}$};
\draw[xz rotated ,vector] (P) --++ (-\myphi:1.5)   node[right] {$\hat{\theta}$};
\draw[xy elevated,vector] (P) --++ (90+\mytheta:3) node[right] {$\hat{\varphi}$};
% point
\fill[point] (P) circle (0.1cm);
\end{tikzpicture}
\end{document}