Question:- Find the volume of solid that lies between planes perpendicular to the axis of symmetry of cone and between $x=0$ to $x=12$. The cross section by planes perpendicular to the axis of symmetry are circular discs whose diameter run from the line $y=\frac{x}{2}$ to the line $y=x$.
If the cross sections were perpendicular to the x-axis then it would be an fairly easy problem of Cavalieri's Theorem.But here cross sections are perpendicular to the axis of symmetry of truncated cone and that's makes it an tough problem.
Equation of axis of symmetry turns out to be $$y=\bigg(\frac{\sqrt{10}-1}{3}\bigg)x$$
I don't know how to integrate after that to find volume as cross sections are neither on x-axis nor y-axis.If we rotate the figure such that axis of symmetry coincides with the x-axis then that also doesn't help.
Thank you for your help!