Let C be the parametrised surface given by
Φ(t,θ)=(cosθ/cosht, sinθ/cosht,t−tanht), for 0≤t and 0≤θ<2π
Let V be the region in R3 between the plane z = 0 and the surface C.
Compute the volume of the region V .
The Attempt at a Solution
I thought I needed to perform a change of variables; changing from x,y,z to theta,t,z.
I tried to find the Jacobean for this, but it came to zero. I'm pretty sure it was wrong in the first place, but I have no idea what to do otherwise. Your assistance would be greatly appreciated.