A solid lies between planes perpendicular to the y-axis at $ y=0$ and $y=1$. The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola $x=\sqrt{11}y^2$. Find the volume of the solid.
The wording of this question really throws me off, should my integral end up being $\int_0^1 π(\sqrt{11}y^2)^2$. Or am I doing this completely wrong?
Thank you for your input!
The diameter runs from the $y$-axis to the parabola $x=\sqrt{11}y^2$. So the radius of cross-section at height $y$ is $\frac{\sqrt{11}y^2}{2}$.
From this radius, you can calculate the area $A(y)$ of cross-section at height $y$, and then find the volume in the usual way.