I have to describe this region in cylindrical coordinates
Ω = {(x,y,z) ∈ R3 ; x2+y2+z2≤1 ; x2+y2≥1−z ; x>0 ; y>0 ; z>0}
With x>0 and y>0 I get θ∈(0,π/2).
My problem comes with the two first restrictions: I know x2+y2=r2, so I have:
And from now on I don't know how to continue to resolve r.
Any help would be much appreciated.
Ω = {(x,y,z) ∈ R3 ; x2+y2+z2≤1 ; x2+y2≥1−z ; x>0 ; y>0 ; z>0}
With x>0 and y>0 I get θ∈(0,π/2).
My problem comes with the two first restrictions: I know x2+y2=r2, so I have:
- r2≤1-z2
- r2≥1-z
And from now on I don't know how to continue to resolve r.
Any help would be much appreciated.