1. The problem statement, all variables and given/known data Let C be a cylinder of radius 1. It is cut by the x-y plane from below, and by the plane z-x=1 above. Parametrize all the surfaces of the cylinder. Find a unit normal (pointing outward) for each surface. 2. Relevant equations Equation for a cylinder: [tex]x^2+y^2=1[/tex] Equation of the plane: [tex]z-x=1[/tex] 3. The attempt at a solution Bottom: [tex]g(r,\theta)=(rcos(\theta),rsin(\theta), 0)[/tex] [tex]n=(0,0,-1)[/tex] Side: I'm not so certain about this one... it should be a function of the height as well as the angle, but I'm not certain how to restrict the angle to depend on the height... I guess something like [tex]x^2+y^2 \le z-x[/tex] I think this is the normal, though... [tex]n=(x,y,0)[/tex] Top: I should compute the intersection of the plane and the cylinder. So I get [tex]x^2+y^2=z-x[/tex] [tex]z=(x-1/2)^2+y^2-1/4[/tex] And what now?