Where did you get this problem? If you are taking a Calculus class in which you are given a problem like this, you should have learned several ways to do problems like this. The simplest, for this problem, is the "disk method". For a specific y value, and the radius of the circle, when rotated around the y-axis, is x. The area of that circle is . Taking "dy" as the thickness of the disk, the volume is . Integrate that. (I suspect that your limits are intended to be . Check it.)