Let $\displaystyle B$ be a ball with radius $\displaystyle a$ and in which the density of any point is equal to the distance to a fixed diameter. Find the mass of the ball.

My attempt : $\displaystyle m=\iiint _{B} \rho (r,\phi, \theta) drd\phi d \theta = \int_0^{2\pi} \int_0^{\pi} \int _0^a r^3 \sin (\phi) drd\phi d\theta=a\pi$.

I had a hard time finding that $\displaystyle \rho (x,y,z)=x^2+y^2$ if I chose the fixed diameter as the $\displaystyle z$-axis. Then I simply converted into spherical coordinates chosing "$\displaystyle r$" instead of "$\displaystyle \rho$" because I already got confused in another exercise because of the notation.

Is my result correct?