Plotting bounded surfaces with conditions

1. Apr 7, 2010

Gameowner

1. The problem statement, all variables and given/known data

Attached question

2. Relevant equations

3. The attempt at a solution

I tried rearranging S1 for Z then using Maple to plot it, which gave me a cone extending from the point z=1.

For S2, would I have to plot it twice? once for <1 and once for =1? I have no idea, any help would be much appreciated

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2. Apr 7, 2010

Staff: Mentor

S2 is a circular disk in the x-y plane. The center of this disk is at (0, 0, 0) and the radius is 1. The equation x^2 + y^2 = 1 represents the circle, and the inequality x^2 + y^2 < 1 represents all the points inside the circle.

3. Apr 7, 2010

Gameowner

Oh! I was confused with the inequality more than anything.

So am I correct if the shape of S1+S2 is a cone? S2 being a disk on the xy-plane and S1 being a cone with the tip on the axis of z at 1, then extended to the xy-plane where it is bounded by S2?

4. Apr 8, 2010

Staff: Mentor

S1 U S2 is sort of cone shaped, with S2 forming the base. I don't think it has the same shape as, say the cone in ice cream cones or in tepees, which have vertical cross sections that are isosceles triangles. I believe that the vertical cross section for the S1 surface curves in and goes up to (0, 0, 1) more steeply.

I haven't graphed it, but that's what I think.

5. Apr 8, 2010

Gameowner

Hey mark44, thank for all your help so far, I went away and plotted the graph again, and this is what I got for S1, is it vaguely correct?

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6. Apr 9, 2010

Staff: Mentor

Yep, looks good.