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Q: Parametrization of surface S ( No Answer,   1 Comment )
Question  
Subject: Parametrization of surface S
Category: Science > Math
Asked by: chuvak2k-ga
List Price: $10.00
Posted: 02 Feb 2005 17:26 PST
Expires: 04 Mar 2005 17:26 PST
Question ID: 467832
x = a*u*cos(2Pi*v), y= a*u*sin(2Pi*v), z= b*v

Describe the parametrized surface S, where a,b are positive constant 0<= u <=1
and 0<= v<= 1   Compute the area of S.
Answer  
There is no answer at this time.

Comments  
Subject: Re: Parametrization of surface S
From: alcatraz28-ga on 08 Feb 2005 21:05 PST
 
OK, here is my answer: the surface is the trace of a stick of length
a, which is being lifted up with velocity b for one second and at the
same time rotated about the z-axis with angular velocity 2Pi.

The surface area can be computed by the standard fomula 
http://ltcconline.net/greenl/courses/202/vectorIntegration/parametricSurfaces.htm
and equals (if I didn't make any mistakes)
(b^2/2Pi) * ln(1+sqrt{2}) + \sqrt{ a^2 * b^2 + 4 * Pi^2 * a^4 * b^2}

Keep the 10 bucks.

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