My guess would be spherical coordinates (slightly modified).
Try
Please, help me to decide this task
Find the volume of a spatial figure which is limited the implicate function:
Please, say: which a system of coordinates I must use?
I tried to use the cylindrical system of coordinates, but a very difficult triple integral.
I used also the generalized spherical coordinates.
There's my solution here.
So, we need find a volume of area , which is limited a surface :
Obviously,
There's a using of the generalized spherical coordinates:
Where , , .
It's jacobian of the transformation:
So, we have [ because ]
where
The calculation of the internal integrals.
So, we have
The integral , calculated by the methods of complex analysis, is equal .
Finally, we have