Finding area between sphere and parabloid

[PsychonautQQ]

Homework Statement

Find the volume above the sphere x^2+y^2+z^2 = 6 and below the parabloid z = 4-x^2-y^2.

Homework Equations

The Attempt at a Solution

I did a triple integral in cylindrical coordinates
Triple Integral: dzdrdθ
where z is between (6-r^2)^(1/2) to (4-r^2) and dr goes from 0 to 2^(1/2) and dθ goes from 0 to 2θ. Are these the proper parameters?

 

[haruspex]

Assuming you meant r, not dr, θ, not dθ, and 2π, not 2θ, yes.