Volume of a solid(between two planes)?

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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!

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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.