size(8cm,0);
import solids;

//Draw 3D right angle (MA,MB)
void drawrightangle(picture pic=currentpicture,
                    triple M, triple A, triple B,
                    real radius=0,
                    pen p=currentpen,
                    pen fillpen=nullpen,
                    projection P=currentprojection)
{
  p=linejoin(0)+linecap(0)+p;
  if (radius==0) radius=arrowfactor*sqrt(2);
  transform3 T=shift(-M);
  triple OA=radius/sqrt(2)*unit(T*A),
    OB=radius/sqrt(2)*unit(T*B),
    OC=OA+OB;
  path3 tp=OA--OC--OB;
  picture tpic;
  draw(tpic, tp, p=p);
  if (fillpen!=nullpen) fill(tpic, O--tp--cycle3, fillpen);
  add(pic,tpic,M);
}

currentprojection=orthographic(100,150,30);
real r=10, h=6; // r=sphere radius; h=altitude section
triple Op=(0,0,h);

real rs=sqrt(r^2-h^2); // section radius
real ch=1-acos(h/r)/pi;

path3 arcD=Arc(O,r,90,0,90,180*ch,Y,32)--(0,0,h);
revolution sphereD=revolution(O,arcD,Z);
sphereD.fill(lightblue);

path3 arcU=Arc(O,r,90,180*ch,90,180,Y,32);
revolution sphereU=revolution(O,arcU,Z);
sphereU.filldraw(opacity(0.5)+lightgrey);

// right triangle OO'A
triple A=rotate(100,Z)*(rs,0,h);
dot("$O$",O,NW);
dot("$O'$",Op,W);
dot("$A$",A,N);
draw(A--O--Op--A);
drawrightangle(Op,O,A);

shipout(format="pdf", bbox(Fill(paleyellow)));