Volume of Solid of Revolution about an equation

I learned about the disk and shell method for finding a volume of a solid of revolution. For my question I don't think I can use either method directly. Here is my question:

Find the volume of the region bounded by $y=x$ and $y={x}^{2}$, but rotated about the equation of $y=x$.

Here the axis of revolution is not a vertical or horizontal line, but rather the equation $y=x$. One idea I had was to convert this diagonal line into a horizontal or vertical one, but I can't see to do this. Maybe polar coordinates might be useful, but I'm not sure.

I learned about the disk and shell method for finding a volume of a solid of revolution. For my question I don't think I can use either method directly. Here is my question:

Find the volume of the region bounded by $y=x$ and $y={x}^{2}$, but rotated about the equation of $y=x$.

Here the axis of revolution is not a vertical or horizontal line, but rather the equation $y=x$. One idea I had was to convert this diagonal line into a horizontal or vertical one, but I can't see to do this. Maybe polar coordinates might be useful, but I'm not sure.