Ever Wondered Why Pyramid Volume Has a 1 3 With Visuals

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Ever Wondered Why Pyramid Volume Has a 1 3 With Visuals

Midnight Math Tutor · ⏱ 2:23 · 2.3K مشاهدة · 9 months ago

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Hey guys, in this video we are going to talk about why the volume of pyramid is 1/3 time the area of the base times the height. The easiest way to illustrate this is to compare it with the volume of cube or rectangular prism. If wanted to find the volume of cube or rectangular prism, would take the area of the base times the height or the length time the width time the height. So now if you compare these, you see they're the same except for this one is being multiplied by 1/3. So let's go ahead and see if we can figure out why that is. If was trying to find the volume of this square pyramid here, one way could think of it is want you to imagine had six of these. But guess what? You don't have to imagine it because actually have it right here. Six of these same pyramids. And look what happens when fold them together. It's actually quite satisfying. It makes this lovely cube. Right now, you'll notice if compare this to my original pyramid, it is double the height, right? Sorry, have to kind of hold it to keep it together. It is double the height, right? And you can see that if you look that it's two pyramids on top of each other, right? So, that's why it's twice the height. So, it has the same base, but it's twice the height. So, want you to imagine that cut this in half. But again, you don't have to imagine it because guess what? have it right here. So, now this is rectangular prism. cut that cube in half. It's rectangular prism that has the same base as my square pyramid and is the same height. If open this up, you can see it's that same pyramid in there. So according to my formula, this one should be three times the volume that this one is. Let's go ahead and open it and see. So when open this up, have one, two, two halves that make the second one, two halves that make the third one. So that is why when we figure out the volume of square pyramid, we take the volume of rectangular prism with the same base and height and multiply it by 1/3. hope this helped. Thanks.