Given the cylinder $(x-1)^2+y^2 \leq1$ and a sphere centred at $(0,0,0)$ with radius $2$, find the volume of the solid formed.

Question

I attempted this using cylindrical co-ordinates but I am not sure if my attempt is correct. This is what I have: equation of sphere : $x^2+y^2+z^2=4,$ cylindrical coordinates this is $z^2=4-r^2$ leading to: $$0.25V= \int_0^{\pi/2} \int_0^1 r\sqrt{4-r^2} \,drd\vartheta$$