For convinent calculation , I locate the center of the circle at

and thus the equation of the circle is

Now , let's go to the integration ,

We know the volume of the revolution about the y-axis is

,

since the distance from the y -axis

we should find x in terms of y , that is

and also

But we know

For the interval , i choose

Now , we are able to see what the integral looks like !

It should be