How to find the volume with the revolution around the $y$ -axis

Question

i need to find the volume formed by rotating the equations around the y axis. My equations are $x=2y$ and $x=y^3$. I have no idea where to start.

Answer 1

$y^3-2y = 0 \to y(y^2-2) = 0 \to y = 0, \pm \sqrt{2}$. Due to symmetry, we can consider $y \geq 0$. Thus: $V = 2\displaystyle \int_{0}^{\sqrt{2}} \pi\left((2y)^2 - (y^3)^2\right)dy$