Use symbolic algebra software to sketch the surface

[jjangub]

Homework Statement

Let S be the union of the two smooth surfaces S1 and S2, where S1={(x,y,z) l x^2+y^2=1, 0\leqz\leq3-sqrt(3)} and S2={(x,y,z) l x^2+y^2+(z-3)^2=4, z\geq3-sqrt(3)}. Use symbolic algebra software to sketch the surface S.

Homework Equations

The Attempt at a Solution

I used Maple to sketch the surface S.
I know how to sketch S1.
I have a problem with S2. It says the error of "the range of z" whenever I tried to sketch S2.
I have no idea how the shape of S2 would be.
Please someone help me.
Thank you very much.

 

[jbunniii]

First, what does this surface look like?

\{(x,y,z) | x^2 + y^2 + (z-3)^2 = 4\}

The surface S2 will be a subset of the above, because it adds a constraint on z.