Maybe my last post wasn't so clear. Sorry about that. Let me rephrase it.

Let's say i have an object bounded by four planes and

And density function of that object is And asked to find first moment of that bounded object about three planes( and plane).

We know from the definition that the first moment of this 3d object about and planes are respectively:

The book without evaluating all three of this, evaluated only and and said that by symmetry The graph of this object is given below. My question is in what way this bounded object is symmetric? And how did they figure that out? Any explanation regarding this question is welcome. I've no idea how they deduced that..

The dark blue surface in the graph below is . And are wireframe planes in rainbow color. And finally wireframe plane is transparent with wireframe visible. If my question isn't clear please let me know.