Surface area of parabolic sheet

[cscott]

Am I correct in saying the surface parameterized by r = (sin v, u, cos v), v = [-pi/2, pi/2], u = [-1, 1] has an area of 2pi ?

I get something different by computing the arc length of the parabola within the bounds and multiplying by 2.

Which method is wrong?

 

[arildno]

Sure, but that is not a parabolic sheet, it is the half-shell of a cylinder with radius 1..

 

[cscott]

Hmm.. I see. Thanks.