Use spherical coordinates to find the volume of the region above the cone z = $\displaystyle \sqrt {x^2 + y^2}$ and between the hemispheres z = $\displaystyle \sqrt {16 - x^2 - y^2}$ and z = $\displaystyle \sqrt {4 - x^2 - y^2}$.

I'm having trouble finding the bounds, would it be

$\displaystyle

\int^{2\pi} _{0} \int^{\frac{\pi}{4}} _{0} \int^{4} _{0}

d\rho d\theta d\phi $