Volume Integration of Bounded Region

I'm trying to integrate this volume in spherical and cylindrical coordinates, but having difficulty finding my bounds of integration;

I'm given the region in the first octant bounded by $z=$ $\sqrt{{x}^{2}+{y}^{2}}$, $z=$ $\sqrt{1-{x}^{2}-{y}^{2}}$, $y=x$ and $y=$ $\sqrt{3}x$ and I need to evaluate ${\iiint}_{V}dV$.

When proceeding to integrate with spherical and cylindrical coordinates I am not getting the right bounds such that both methods equate to the same volume? I am definitely missing something. Any and all advice would be much appreciated!

I'm trying to integrate this volume in spherical and cylindrical coordinates, but having difficulty finding my bounds of integration;

I'm given the region in the first octant bounded by $z=$ $\sqrt{{x}^{2}+{y}^{2}}$, $z=$ $\sqrt{1-{x}^{2}-{y}^{2}}$, $y=x$ and $y=$ $\sqrt{3}x$ and I need to evaluate ${\iiint}_{V}dV$.

When proceeding to integrate with spherical and cylindrical coordinates I am not getting the right bounds such that both methods equate to the same volume? I am definitely missing something. Any and all advice would be much appreciated!