Let A={ (x,y,1) | x²+y² <=1 }, B={ (x,y, -1) | x²+y² <=1 },
L = { segment PQ | P( cos(t), sin(t), 1 ), Q( cos(t+a), sin(t+a), -1 ) for any t },
where a is a constant and 0 < a < π.
then L forms a surface S, find
(1) the equation of the surface S
(2) the volume of the region enclosed by the surface S, A and B
(3) the area of the surface S.