Is this correct sytntax: the slice is a semicircle **parallel** to the x axis when perpendicular to y with triangle base along the x and y axes?

Question

I just took an exam and the question was this:

Find the volume where the base is a triangle with the vertices: (0,0),(4,0),& (0,4). The cross section is a semicircle and is perpendicular to the y-axis and is parallel to the x-axis.

I get everything up to the "parallel to the x-axis" part. Okay, so we are not using the z-axis for this course but isn't the cross-section parallel to the z-axis?

Okay, so I guess the professor was talking about was the base of the cross-section, not the cross-section.

I get that.

However, I have looked around the internet and in my multiple text books and I have never seen this type of problem explained as "parallel to the x-axis" so I want to know if this is incorrect syntax.

If the base is along the x and the y axis, how is the cross-section itself parallel to x?

Answer 1

Why not simpler

A triangle has vertices: O (0,0),X(4,0),& Y (0,4). Find half cone volume enclosed when triangle $YOX$ (slant line and base radius) are rotated $180^0$ about y-axis.