Which of the following solids have a volume=the integral of 2x dx from 0 to 2 ?

I. A solid whose base is a region bounded by y=x/2, y=-x/2 and x = 2, whose cross-sections are perpendicular to the x-axis are squares.
II. A four-sided pyramid whose base is a square with area 4 and whose height is 2.
III. A solid formed when the region bounded by the x-axis, y=x/2 and x = 2 is revolved about the x-axis.

Question

Which of the following solids have a volume=the integral of 2x dx from 0 to 2  ?

I. A solid whose base is a region bounded by    y=x/2, y=-x/2 and x = 2, whose cross-sections are perpendicular to the x-axis are squares.
II. A four-sided pyramid whose base is a square with area 4 and whose height is 2.
III. A solid formed when the region bounded by the x-axis, y=x/2 and x = 2 is revolved about the x-axis.

anonymous · Answer

1) I
2) II
3) II and III
4) I and II
5) I, II, and III

anonymous · Answer

You can immediately eliminate the third option because a solid of revolution will tend to have a volume in terms of $\pi$ if the function in question is not, which means (3) and (5) can't be right.

anonymous · Answer

Here's a sketch of the base of the solid described in (I)
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