Bsrgvty

As described above, I want to draw the finishing touch by drawing the blue, curved line so that the finished image looks like a slice of a cake.

Thank you.

What I have so far:

documentclass[]article
usepackage[margin=0.5in]geometry
usepackagepgfplots
renewcommandthesectionarabicsection
usepackagemathtools
usepackagecancel
usepackagepgfplots
usepackageamsmath
newtheoremtheoremTHEOREM
newtheoremproofPROOF
usepackagetikz
usepackageamssymb
usetikzlibrarypatterns
usepackagefancyhdr
usepackagebigints
usepackagecolor
usepackagetcolorbox
usepackagecolor,xcolor
usepackagebooktabs,array
usepackagehyperref
usepackagegraphicx
usetikzlibraryarrows
usepackagepolynom
usepackageflexisym
usepackagewallpaper
usepackageblkarray
usepackagecaption
usepackagelscape
usepgfplotslibraryfillbetween
usepgfplotslibrarystatistics
usetikzlibraryshapes.misc
usetikzlibraryarrows.meta
newenvironmenttightcenter
setlengthtopsep0pt
setlengthparskip0pt
begincenterendcenter
begindocument
begintikzpicture
%draw[thick] (0,0) circle (4.5cm);
%draw[fill=black] (0,0) circle (0.3mm);
%node[below] at (0,0)$O$;
%node[below] at (1.25,0.9)$2$ cm;
%node[below] at (-0.9,0.9)$2$ cm;
%
%draw[thick,color=black,fill=gray!30] (0,0) -- (120:4.5) arc(120:45:4.5) -- cycle;
draw[thick,color=black,fill=gray!30] (0,0) -- (-20:4.5) arc(-20:-50:4.5) -- cycle;
draw[thick,color=blue!30] (-35.5:5.2) arc(-35.5:-60:5.2);
draw[thick,color=black] (4.23,-1.55) -- (4.23,-3.52);
draw[thick,color=black] (2.9,-3.43) -- (2.9,-4.67);
draw[thick,color=black] (0,0) -- (0,-1.04)-- (2.9,-4.67);
%
%draw [thick,<->] (0.28,-0.4) -- node[fill=white] small $2$ textcm (2.12,1.33);
%draw [thick,<->] (-0.5,-0.3) -- node[fill=white] small $2$ textcm (-1.73,1.83);
%
endtikzpicture
enddocument

Like this ?

To avoid having to manually calculate the coordinates of the points, I use the relative positioning of the points with the syntax --++.
This syntax indicates that to obtain the coordinates of the next point, we add the preceding point (0,-1.24)

(4.23,-1.55) --++ (0,-1.24)

is equivalent to

(4.23,-1.55) -- (4.23,-2.79)

indeed 4.23 + 0 = 4.23 and -1.55 + (-1.24) = -2.79

documentclass[tikz,border=5mm]standalone

begindocument
begintikzpicture
draw[thick,color=black,fill=gray!30] (0,0) -- (-20:4.5) arc(-20:-50:4.5) -- cycle;
draw[thick,color=black,yshift=-1.24cm] (-20:4.5) arc(-20:-50:4.5) -- (0,0);
draw[thick,color=black] (4.23,-1.55) --++ (0,-1.24);
draw[thick,color=black] (2.9,-3.43) --++ (0,-1.24);
draw[thick,color=black] (0,0) --++ (0,-1.24);

endtikzpicture
enddocument

If you use tikz-3dplot, you do not have to guess the curves, and you can adjust the view angles at will.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot
begindocument
tdplotsetmaincoords7560
begintikzpicture[tdplot_main_coords]
beginscope[canvas is xy plane at z=0,name prefix=bot-]
 draw (0,0) coordinate (O) -- (4,0) coordinate (A) arc (0:60:4) coordinate
 (B);
endscope 
beginscope[canvas is xy plane at z=2,name prefix=top-]
 draw[fill=blue!20] (0,0) coordinate (O) -- (4,0) coordinate (A) arc (0:60:4) coordinate
 (B) -- cycle;
endscope 
 draw foreach X in O,A,B
 (bot-X) -- (top-X);
endtikzpicture
enddocument

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot
begindocument
foreach X in 89,88,...,60,61,62,...,88
tdplotsetmaincoords70+10*sin(6*X)X
pgfmathsetmacroxmin0
pgfmathsetmacroxmax0
pgfmathsetmacroymin0
pgfmathsetmacroymax0
begintikzpicture[tdplot_main_coords]
 ifdefinedfigbbrelax
 path figbb;
 fi
 beginscope[canvas is xy plane at z=0,name prefix=bot-]
 draw (0,0) coordinate (O) -- (4,0) coordinate (A) arc (0:60:4) coordinate
 (B);
 endscope 
 beginscope[canvas is xy plane at z=2,name prefix=top-]
 draw[fill=blue!20] (0,0) coordinate (O) -- (4,0) coordinate (A) arc (0:60:4) coordinate
 (B) -- cycle;
 endscope 
 draw foreach X in O,A,B (bot-X) -- (top-X);
 path let p1=(current bounding box.south west),
 p2=(current bounding box.north east)
 in pgfextra%
 pgfmathsetmacroxminmin(x1,xmin)
 pgfmathsetmacroxmaxmax(x2,xmax)
 pgfmathsetmacroyminmin(y1,ymin)
 pgfmathsetmacroymaxmax(y2,ymax)
 xdefxminxmin pt
 xdefxmaxxmax pt 
 xdefyminymin pt
 xdefymaxymax pt 
 ; 
endtikzpicture
makeatletter 
edeffigbb(xmin,ymin) rectangle (xmax,ymax)
immediatewrite@mainauxxdefstringfigbbfigbbrelax
makeatother
enddocument

If you want to allow for arbitrary view angles, you need to distinguish some cases as in this answer which provides you with the rest of the (cheese) cake (except for the piece stolen by the mouse;-).

One more example: In the drawing, angles are considered in reverse order. For vertical lines, the coordinate is defined, so that only one coordinate now is necessary to determine of height of slice:

documentclass[tikz, margin=3mm]standalone

begindocument
 begintikzpicture[
every path/.style = thick, line join=round % style of lines
 ]
draw[fill=gray!30] (0, 0) -- (-50:4.5) coordinate (a1) arc(-50:-20:4.5) coordinate (a2) -- cycle;
draw (0,0) -- (0,-2) % determine height of slice
 -- ++(-50:4.5) coordinate (b1) arc(-50:-20:4.5) coordinate (b2);
draw (a1) -- (b1) (a2) -- (b2);
 endtikzpicture
enddocument