Find the volume of $\omega=\{(x,y,z) | x^2+y^2+z^2\leq a^2 , x^2+y^2\leq ax\}$
$x^2+y^2+z^2\leq a^2 \implies x^2+y^2\leq a^2-z^2$.
Therefore , $a^2-z^2 \leq ax \implies a^2-ax\leq z^2$.
Using substitution $x=a\sin\theta \cos\phi, y=a\sin\theta \sin\phi, z=a\cos\theta, a>0,0\leq \theta\leq \pi ,0\leq \phi\leq 2\pi$.
$a^2-ax\leq z^2 \implies a^2-a(a\sin\theta \cos\phi)\leq a^2\cos^2\theta \implies 1-\sin\theta\cos\phi\leq \cos^2\theta$.
I don't know how to solve this problem and find the limits of the integral , any help please.