How to Calculate the Moment of Inertia of a Pyramid Along the Z Axis?

physicsnoob93
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Homework Statement


Ok not really a school problem but i was just thinking of how to solve it.

How would i find the moment of inertia of a pyramid with base side length l and height h?
If the axis of rotation is along the z axis?


Homework Equations



I = Summation of mrsquared

The Attempt at a Solution



Ok so my approach is to find the geometrical center of the pyramid first.

I would know its easy to cut each of the diagonal lengths by 2 and drawing a straight perpendicular line down, but i wanted to try some integration because i just learned it a week ago.
I had problems setting up the integral, so could anyone give me a hint or 2?
 
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I would start by finding the moment of inertia of a triangular cross section of the pyramid at height z and thickness dz and then integrate that.
 
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