triple intergral

Question

An engine part is a solid S in the shape of an Egyptian-type pyramid having height 2 and a square base with diagonal D of length 2. Inside the engine it rotates about D. Set up an iterated integral giving its moment of inertia about D. Assume   δ=1. Place S so the positive z axis is its central axis. 

Answer 1

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Answer 2

Sue,

 

I recently posted a reply to one of your questions similar to this one (the moment of inertia of the "ice cream cone").

 

Since the solid does not have any rotational symmetry, I recommend using the same formula I gave in that post, but use rectangular coordinates only. You will need to describe the pyramid as a solid in Cartesian coordinates correctly.

 

Let me know if you need more help with the set up. These questions are hard to explain using only the medium of a chat box, which is why I prefer to ask you for more input before I offer any more help myself.