this is not a volume, just a triple integral \(\displaystyle a>0\) and \(\displaystyle b>0\) in spherical coordinates \(\displaystyle \int _0^{2\pi }\int _0^{\arctan (1/a)}\int _0^b\rho ^4\sin \phi d\rho d\phi d\theta =\frac{2}{5} \left(1-\frac{a}{\sqrt{1+a^2}}\right) b^5 \pi\) in cylindrical coordinates \(\displaystyle \int _0^{2\pi }\int _0^{\frac{b}{\sqrt{a^2+1}}}\int _{a r}^{\sqrt{b^2-r^2}}\left(r^2+z^2\right)rdzdrd\theta =\frac{2}{5} \left(1-\frac{a}{\sqrt{1+a^2}}\right) b^5 \pi\)