# Volume of a solid(between two planes)?

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?

• @Semiclassical, is this the plot you are looking for? I've used the equation $$\sqrt{(x-\sqrt{11}y^2/2)^2+z^2}=\sqrt{11}y^2/2$$ – cutculus Jul 19 '14 at 4:12
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.