How do I prove that the volume of a rectangular pyramid is divided by 3? @Zarkon
Stacey Warren - Expert brainly.com
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this video might help
What I've got so far is that.. |dw:1444608594950:dw|
So when I was thinking about it... the sides of a rectangular prism make half of a pyramid, therefore if we combined them together that would give us 1 full pyramid, and then the sides of the rectangular prism make 2 more triangular prisms altogether equalling 3.
Does my method make any sense to anyone?
And thanks Jim! I was trying to figure it out on my own,this is how far I've gotten :) lol.
Ahh... I was approaching this without calculus haha
i spose h=zmax in this case ...
might have a bad change of variable is all
How did you find \(x=kz\) and \(y=nz\)? are \(k\) and \(n\) just scaling factors?
to make life simpler i turned the pyramid upside down so that the lines defined would go thru the origin is all
allowing k and n to account for any width/depth and z for the height
the volume of any slice being xy dz, or dh for a dummy variable
I'll bbs. afking for a moment.
Start with a cube.
Think of a point in the center of the cube.
Each face of the cube is the base of a pyramid, and the center of the cube is the vertex.
There are 6 congruent pyramids.
Each pyramid is 1/6 of the volume of the cube.
If you now think of half of the cube, which has the same height as the pyramid inside, the pyramid is 1/6 the volume of the original cube or 1/3 the volume of half of the cube.