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.