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+import solids;
+size(0,150);
+currentprojection=perspective(0,0,10,up=Y);
+pen color=green;
+real alpha=240;
+
+real f(real x) {return x^2;}
+pair F(real x) {return (x,f(x));}
+triple F3(real x) {return (x,f(x),0);}
+
+path p=graph(F,0,1,n=10,operator ..)--cycle;
+path3 p3=path3(p);
+
+render render=render(compression=0,merge=true);
+
+draw(surface(revolution(p3,Y,0,alpha)),color,render);
+
+surface s=surface(p);
+draw(s,color,render);
+draw(rotate(alpha,Y)*s,color,render);
+
+draw(p3,blue);
+
+xaxis3(Label("$x$",1),Arrow3);
+yaxis3(Label("$y$",1),ymax=1.25,dashed,Arrow3);
+
+dot("$(1,1)$",(1,1,0),X);
+arrow("$y=x^{2}$",F3(0.7),X,0.75cm,red);
+arrow("$y=x$",(0.8,0.8,0),Y,1cm,red);
+
+real r=0.4;
+draw((r,f(r),0)--(r,r,0),red);
+draw("$r$",(0,(f(r)+r)*0.5,0)--(r,(f(r)+r)*0.5,0),N,red,Arrows3,PenMargins3);
+draw(arc(1.1Y,0.3,90,0,7.5,180),Arrow3);