> x:=cos(t):

> y:=sin(t):

> z1:=x:z2:=-x:

> z:=(1-s)*z1+s*z2:

> a:=plot3d([x,y,z],s=0..1,t=0..2*Pi,scaling=constrained,color=yellow):

> b:=plot3d([z,y,x],s=0..1,t=0..2*Pi,scaling=constrained,color=red):

> with(plots):

Warning, the name changecoords has been redefined

> with(plottools):

> vrml(c,"d:/87116/16101.wrl",background_color=white);

>

2 Construct the portion of the cylinder x^2 + z^2 = 0.81 lying outside x^2 + y^2 =1.

> restart;

> with(plots):with(plottools):

Warning, the name changecoords has been redefined

> z:=0.9*sin(t):

> y1:=(1-x^2)^(1/2):y2:=1.5:

> y:=(1-s)*y1+s*y2:

> a:=plot3d([x,y,z],s=0..1,t=0..2*Pi,scaling=constrained,color=red):

> b:=plot3d([x,-y,z],s=0..1,t=0..2*Pi,scaling=constrained,color=red):

> x:=cos(t):

> y:=sin(t):

> z1:=(0.81-x^2)^(1/2):z2:=-z1:

> z:=(1-s)*z1+s*z2:

> u:=arccos(0.9):

> c:=plot3d([x,y,z],s=0..1,t=u..(Pi-u),scaling=constrained,color=yellow):

> d:=plot3d([x,-y,z],s=0..1,t=u..(Pi-u),scaling=constrained,color=yellow):

> with(plottools):

> e:=display(a,b,c,d):

> vrml(e,"d:/87116/16102.wrl",background_color=white);

3 Construct the solid bounded by the parabolic cylinder
z = 4 - y^2
and the elliptic paraboloid
z = x^2 + 3y^2

> restart:

> x:=2*r*cos(t):y:=r*sin(t):

> z:=4-y^2:

> a:=plot3d([x,y,z],t=0..2*Pi,r=0..1,scaling=constrained,color=red):

> z:=x^2+3*y^2:

> b:=plot3d([x,y,z],t=0..2*Pi,r=0..1,scaling=constrained,color=blue):

> with(plots):

Warning, the name changecoords has been redefined

> with(plottools):

> vrml(c,"d:/87116/16103.wrl",background_color=green);

4 Construct the Astroidal Ellipsoid given by
x = (cos(u)cos(v))^3,
y = (sin(u)cos(v))^3
z = sin(v)^3

> restart:

> x:=(cos(u)*cos(v))^3:

> y:=(sin(u)*cos(v))^3:

> z:=(sin(v))^3:

> c:=plot3d([x,y,z],u=0..2*Pi,v=0..2*Pi,scaling=constrained,grid=[35,35]):

> with(plottools):

> vrml(c,"d:/87116/16104.wrl",background_color=yellow);

5 Construct this surface:

> restart:

> x:=r*cos(t):y:=r*sin(t):r:=0.1*t:

> c:=plot3d([s*x,s*y,2*(1-s)],s=0..1,t=0..40,grid=[5,200],scaling=constrained,color=COLOR(RGB,0.3,0.5,0.2)):

> with(plottools):

> vrml(c,"d:/87116/16105.wrl",background_color=yellow);

6 Construct this surface:

> restart:

> r:=exp(-t):x:=r*cos(s):y:=r*sin(s):

> z:=t+0.2*s:

> c:=plot3d([x,y,z],s=0..8*Pi,t=0..3,grid=[100,20],scaling=constrained,color=COLOR(RGB,0.5,0.3,0.2)):

>