Volume of a Pyramid Formula in 3 D

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in mathematics we often solve for but what about you may or may not know that the formula for finding the volume of pyramid with square base is one-third times the area of the base times the height today want to show you visual representation of this so we can see where this formula actually comes from as reminder the volume of cube is length times width times height and since the area of square is length times width we can shorten this formula to be the area of the base times the height and as it turns out we can actually split this cube apart into three equally sized pyramids with square bases and as you can see the height of each pyramid is the same as the height of the cube and since the volume of cube is the area of the base times the height and we just split this cube into three equal pieces then the volume of each of these pyramids will be one-third times the area of the base times the height and that's one way to visually represent the formula for the volume of pyramid with square base another way we could show this is by splitting the cube into six identical pyramids with square bases then each pyramid's volume will be 1 6 the volume of cube or in other words 1 6 times the area of the base times the height of the cube but you'll notice that the height of the cube is twice as tall as the height of the pyramid so we can replace this height which represents the height of the cube with 2 times the height of the pyramid and simplifying this equation we will once again get 1 3 times the area of the base times the height of the pyramid you may have seen the formula for the volume of pyramid with square base before and been curious as to where that one third comes from and hope that these visual representations might help you see that better this was what about you