Spherical or Cylindrical coordinates?



I have the function f(x,y,z) = y on the domain:

{(x,y,z) | 0 <= y, x2+ y2 + z2 <= 1}

I would like to find the volume integral but should I convert the domain to Spherical or Cylindrical coordinates first? I assume the domain should also be converted to an elementary domain?
.