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Center of Mass of a 4D Pyramid Using Calculus

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Find the center of mass of a 4D pyramid (cube base) using calculus.

Explanations, step-by-step procedure, diagram if possible.

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The center of mass of a 4-D pyramid is found using calculus. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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The calculus proof starts similar to the N-slices proof:
We assume the pyramid is straight, that its side edges are all of the same length and its 4-height connects its top with the center of the base cube.
The center of mass (COM) of a cube is in the cube's center.
Let the base cube have side A, then its 3D volume is ...

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