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The volume of a triangular pyramid is 1/3 that of a triangular prism that is the same height, and has an equal sized base.
In order to demonstrate this fact I used a triangular shaped plastic prism and pyramid and filled them with water. What you will see is that when you fill the pyramid up with water, and pour this amount into the prism , that it takes exactly three pyramids to fill one prism.
Hopefully this visual demonstration will help you understand how the formulas for finding the volume of a prism and pyramid are derived.
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