Thread: Volume by cross-sections (possibly misleading)

The basis of a solid is the circle . Every cross-section perpendicular to the x axis is a rectangle whose height is twice the distance from the origin of the circle to the plane of the cross-section. Find the volume of the solid.

Note: I don't know what the problem means by "origin of the circle". I assumed it means the center of the circle, (8,0), but I think it could mean instead the origin (0,0).

This is my reasoning: the distance mentioned is , so the height of a cross-section is , assuming . The length of a cross-section is , so the cross-sectional area is . Integrate this from x = 0 to x = 8, multiply by 2 to cover the other half of the solid and you find . But the answer is supposed to be or something like that.

Is this right? Is the problem misleading? Any help would be greatly appreciated.

horizontal distance from the origin (0,0) to a representative cross-section is x.

area of a representative cross-section ...