Calculate the volume of a part of a sphere inside a cylinder

Find the volume of the part of the sphere which is inside the cylinder where are the cylindrical coordinates.

My attempt : I'm not able to visualize the sphere nor the cylinder.

For the sphere, does ? If so then I can imagine the sphere. (Centered at the origin and with radius ).

For the cylinder I don't know how to go further. I also feel it's useless to convert all in Cartesian coordinates but this way it's easier to me to visualize the volumes.