Finding the volume of revolution obtained by rotation of a region about the line $2x-y=20$

Question

I have the following question before me: Find the volume of the area bounded by the curves $y=x^3$, $x+y=10$ and $x=0$ about the line $2x-y=20$. I started off by drawing the given area and line of rotation. I found out the point of intersection as $(2,8)$. But I do not know how to proceed from there. I tried doing it in terms of perpendicular distances from the line of rotation taking the point $(8,-4)$ as new origin. I obtained this point $(8,-4)$ by drawing a perpendicular on the line of rotation from origin and then finding out the point of intersection of the two lines. But that seemed too daunting a task to me. Is there some (other) nicer method to evaluate this volume? Please suggest. I have shown my work in an attached image. I have to just set up the double integral and not actually compute it.