Btukfyl

I'm still trying to get the hang of tikz.
I'm trying to shade a calotte within a sphere.
The code

begin{tikzpicture}[font = sansmath]

  coordinate (O) at (0,0);







  % ball background color

  shade[ball color = blue, opacity = 0.1] (0,0) circle [radius = 2cm];



  % cone

  begin{scope}

    defrx{0.71}% horizontal radius of the ellipse

    defry{0.15}% vertical radius of the ellipse

    defz{0.725}% distance from center of ellipse to origin



    path [name path = ellipse]    (0,z) ellipse ({rx} and {ry});

    path [name path = horizontal] (-rx,z-ry*ry/z)

                                -- (rx,z-ry*ry/z);

    path [name intersections = {of = ellipse and horizontal}];





  end{scope}





  % ball

  draw (O) circle [radius=2cm];

  % label of ball center point

  filldraw (O) circle (1pt) node[below] {$O$};



  % radius

  draw[densely dashed] (O) to [edge label = $1$] (-1.33,1.33) coordinate (x);

  draw[densely dashed] (O) -- (1.33,1.33) coordinate (y);



  % cut of ball surface

  draw[red, densely dashed] (-1.36,1.46) arc [start angle = 170, end angle = 10,

    x radius = 13.8mm, y radius = 3.6mm];

  draw[red] (-1.29,1.52) arc [start angle=-200, end angle = 20,

    x radius = 13.75mm, y radius = 3.15mm];



  % label of cut of ball surface

  draw (-1.2,2.2) -- (-0.23,1.1) node at (-1.37,2.37) {$B$};



  %angle

  pic[draw,->,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"][blue] {angle=y--O--x};



end{tikzpicture}

gives me the sphere I'm working with and I want to have that:

I've tried fiddling with shade to no success.

Like this?

documentclass[tikz,border=3.14mm]{standalone}

usepackage{sansmath}

usepackage{tikz-3dplot}

usetikzlibrary{3d,backgrounds,quotes,angles,calc,patterns}

begin{document}

tdplotsetmaincoords{80}{00}

begin{tikzpicture}[tdplot_main_coords,font=sansmath]

 pgfmathsetmacro{R}{2} % radius

 pgfmathsetmacro{myang}{50} % latitude angle of the red circle

 coordinate (O) at (0,0,0);

 shade[ball color = blue, opacity = 0.2,tdplot_screen_coords] 

 (O) circle [radius = R*1cm];

 begin{scope}[canvas is xy plane at z={R*sin(myang)},transform shape]

  % angVis from https://tex.stackexchange.com/a/49589/121799

  pgfmathsetmacroangVis{atan(sin(myang)*cos(tdplotmaintheta)/sin(tdplotmaintheta))}

  begin{scope}[on background layer]

   draw[red,dashed] (angVis:{R*cos(myang)}) arc (angVis:180-angVis:{R*cos(myang)});

  end{scope}  

  draw[red] (180-angVis:{R*cos(myang)}) arc (180-angVis:360+angVis:{R*cos(myang)});

  path (0:{R*cos(myang)}) coordinate (R) 

  (180:{R*cos(myang)}) coordinate (L);

 end{scope}

 begin{scope}[on background layer]

  draw[dashed] (L) -- (O) node[midway,below] {$L$} -- (R);

  fill (O) circle[radius=1pt] node[below] {$O$};

  pic[draw,-latex,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"] 

  {angle=R--O--L};

 end{scope}

 path[tdplot_screen_coords,pattern=north east lines,pattern color=green!70!black] 

 let p1=(L),p2=(R),n1={atan2(y1,x1)},n2={atan2(y2,x2)}

 in (O) -- (R) arc(n2:n1:R) -- cycle;

end{tikzpicture}

end{document}

You can, of course, also add this to your code (which I find a bit more complicated than necessary, but this is only my opinion).

documentclass[tikz,border=3.14mm]{standalone}

usepackage{sansmath}

usetikzlibrary{quotes,angles,%intersections,%<- not used

calc,patterns}

begin{document}



begin{tikzpicture}[font = sansmath]

  coordinate (O) at (0,0);







  % ball background color

  shade[ball color = blue, opacity = 0.1] (0,0) circle [radius = 2cm];



  % cone you are not using this anywhere

%   begin{scope}

%     defrx{0.71}% horizontal radius of the ellipse

%     defry{0.15}% vertical radius of the ellipse

%     defz{0.725}% distance from center of ellipse to origin

% 

%     path [name path global=ellipse]    (0,z) ellipse ({rx} and {ry});

%     path [name path = horizontal] (-rx,z-ry*ry/z)

%                                 -- (rx,z-ry*ry/z);

%     

% 

% 

%   end{scope}





  % ball

  draw (O) circle [radius=2cm];

  % label of ball center point

  filldraw (O) circle (1pt) node[below] {$O$};

  % radius

  draw[densely dashed] (O) to [edge label = $1$] (-1.33,1.33) coordinate (x);

  path[fill=green!70!black,fill opacity=0.5] 

    (O) -- (45:2) arc(45:135:2cm) -- cycle;

  draw[densely dashed] (O) -- (1.33,1.33) coordinate (y);



  % cut of ball surface

  draw[red, densely dashed] (-1.36,1.46) arc [start angle = 170, end angle = 10,

    x radius = 13.8mm, y radius = 3.6mm];

  draw[red] (-1.29,1.52) arc [start angle=-200, end angle = 20,

    x radius = 13.75mm, y radius = 3.15mm];



  % label of cut of ball surface

  draw (-1.2,2.2) -- (-0.23,1.1) node at (-1.37,2.37) {$B$};



  %angle

  pic[draw,->,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"][blue] {angle=y--O--x};

end{tikzpicture}

end{document}