import three;
import graph3;
import solids;
size(8cm);
triple sp(real r, real t, real p) { return (r*Sin(p)*Cos(t),r*Sin(p)*Sin(t),r*Cos(p)); }

currentprojection=perspective((30,20,30));
currentlight = light(lightgray,ambient=white,specular=white,
                     specularfactor=3,(30,30,20));

real R = 2;
real r = 1;

path3 p1 = Arc((0,0,0),R,0,0,90,0);
path3 p2 = Arc((0,0,0),R,90,0,180,0);
surface s1 = surface(revolution((0,0,0),p1,90,360));
surface s2 = surface(revolution((0,0,0),p2,0,360));
draw(s1,lightblue);
draw(s2,lightblue);
draw(unitsphere,lightblue+opacity(.4));

path3 g1 = (2,0,0)--(1,0,0)--arc((0,0,0),1,90,0,0,0)--(0,0,2)--arc((0,0,0),2,0,0,90,0)--cycle;
path3 g2 = (0,2,0)--(0,1,0)--arc((0,0,0),1,90,90,0,90)--(0,0,2)--arc((0,0,0),2,0,90,90,90)--cycle;
path3 g3 = (2,0,0)--(1,0,0)--arc((0,0,0),1,90,0,90,90)--(0,2,0)--arc((0,0,0),2,90,90,90,0,normal=(0,0,1))--cycle;
draw(surface(g1),lightgrey);
draw(surface(g2),lightgrey);
draw(surface(g3),lightgrey);

label("$V$",(.5,.1,1.5));
draw((0,0,0)--(0,2/sqrt(2),2/sqrt(2)),Arrow3);
draw(Label("$R_1$",MidPoint,W),(0,0,0)--sp(1,60,90),Arrow3);
label("$R_2$",(.1,.9,1.3));
triple a = (-1/2,sqrt(15/8),sqrt(15/8));
triple b = 1.5*a;
triple a2 = sp(1,90,65);
triple b2 = a2*3.5;
draw(Label("$S_2$",EndPoint),a--b);
draw(Label("$S_1$",EndPoint),a2--b2);
xaxis3(Label("$x$"),xmin=0,xmax=2.75,red,Arrow3);
yaxis3(Label("$y$"),ymin=0,ymax=2.75,red,Arrow3);
zaxis3(Label("$z$"),zmin=0,zmax=2.75,red,Arrow3);