Finding Volume using spherical coordinates

Question: Find the spherical coordinate limits for the integral that calculates the volume of the solid between the sphere $\displaystyle \rho=4 cos\phi$ and the hemisphere $\displaystyle \rho=6, z\geq0$. Then evaluate the integral.

I found the integral with the correct limits for the solid in spherical coordinates as the following: $\displaystyle V=\int_{0}^{2\pi}\int_{0}^{\pi/2}\int_{4cos\phi}^{6} \rho^2 sin\phi\,d\rho d\phi d\theta $

I would like to check my volume, the answer which i got is $\displaystyle \frac{26\pi}{3}$.