Parameterizing a cone between z=2 and z=3

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Lancelot59
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I'm given a problem where I need to parameterize a cone, but only the segment between two planes, being z=2 and z=3.

This is what I ended up with:

[tex]r(u,v)=(ucos(v),u(sin(v),u)[/tex]
[tex]u:[2,3][/tex]
[tex]v:[0,2\pi][/tex]

Is this right?
 
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Alrighty then, thanks.