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Determine allowable values in the torus: y = Sqrt[(r^2 - (x - R)^2)]?

Posted 9 years ago

I'm doing a project for my calculus class where we are determining the volume and surface area of a torus.The question I am on is asking me to find the allowable values of "R' and 'r' in the equation y=Sqrt[(r^2 - (x - R)^2)]. It gives us the manipulate shown below, but it does not work. I can manipulate "R" just fine, but when I try to move "r," the picture disappears. Could somebody tell me if this is typed in wrong? Or is there another way to solve this problem?

What I typed in:

Manipulate[
 ParametricPlot3D[
  {(R + r Cos[\[Alpha]]) Cos[\[Theta]], (R + 
      r Cos[\[Alpha]]) Sin[\[Theta]], r Sin[\[Alpha]]}, {\[Alpha], 0, 
   2 \[Pi]}, {\[Theta], 0, 2 \[Pi]},
  PlotPoints -> 50, ImageSize -> Small, Mesh -> None,
  {Axes -> False, Boxed -> False}, PlotStyle -> Brown, 
  ImageSize -> 200],
 {R, 0.2, 0.629961}, {r, 0.2, radiusr}]
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POSTED BY: Stephen Fedewa
3 Replies
Posted 9 years ago

You are right, about the cos[alpha] part, in that the way it's shown is just the way the site shows it. Though I'm still unsure how to solve the problem. To be more specific, the problem states "Find the range of allowable values for R and r, with 0.2<r<0.629961." I think the problem may be with the "radiusr" part at the end of the code.

POSTED BY: Stephen Fedewa
Posted 9 years ago

I should also specify that the volume of the torus has to be fixed at (pi^2)/2

POSTED BY: Stephen Fedewa
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Posted 9 years ago
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