Find the volume of intersection between cylinders 
Find the volume of intersection of the cylinder
   {$ x^2 + 
y^2 \leq 1 $} , {$ x^2 + z^2 \leq 1$}, {$ y^2 + z^2 \leq 1$}.

i am having tough time finding the volume how do i solve this kind of questions ? .
my trial :
i will move to the cylinder coordinates of the xy cylinder let :
$x^2 + y^2 = r^2 $
$ z = z $
$0\leq\theta \leq 2\pi$
solving the inequalties i get :
$ 0 \leq r^2 \leq 1$ 
$ -\sqrt{1-\frac{r^2}{2}}\leq z \leq \sqrt{1-\frac{r^2}{2}}$
$0\leq\theta \leq 2\pi$
the integral is :
$ \int_{z=-\sqrt{1-\frac{r^2}{2}}}^{z=\sqrt{1-\frac{r^2}{2}}}\int_{r=0}^{r=1}\int_0^{2\pi} dz \ dr \ d{\theta}$ = $ \frac{4\pi}{\sqrt{2}}\frac{(2-r^2)^{\frac{3}{2}}}{-3} |_{r=0}^{r=1}$


$$V = 16 \int\limits_0^{\pi/4} \int\limits_0^1 s \sqrt{1 - s^2 \cos^2 \theta}\ ds\ d\theta = 8(2 - \sqrt{2}) $$
