Calculate $\int\limits_{-1}^1\int\limits_{-\sqrt{1-y^2}}^1\int\limits_{-1}^1(x^2+y^2)^{3/2}\,dz\,dx\,dy$

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How to integrate this using cylindrical coordinates:

$$\int_{-1}^1\int_{-\sqrt{1-y^2}}^1\int_{-1}^1(x^2+y^2)^{3/2}\,dz\,dx\,dy$$

Now what I can understand is that we can directly integrate the $z$ part. Now I am confused in transferring the $x$ part from $(x,y,z)$ to $(r,\theta,z)$ as here $\theta$ will vary from $0$ to $2\pi$ but what about the $r$ part?

Please help.