I assume this means that the radius goes from one side of the circle to the other for the given value of x which the plane lies on.one of its radii in the base
If the plane lies perpendicular to the x axis then is crosses the x axis at only one point.
For a given point x where the plane crosses the x axis the "height" of the circle is (if you draw a 2D diagram of the circle with the y axis in the upwards direction then it is more clear what I mean by height)
The radius of the quarter circle at this point will be .
The area of the quarter circle will be .
The volume of a small slice of the quarter circle is dV. .
Integrate the volume between the values of x where a plane crosses the circle to get the volume of the solid