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- Jhannybean

How do I prove that the volume of a rectangular pyramid is divided by 3? @Zarkon

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

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- jim_thompson5910

this video might help
https://www.youtube.com/watch?v=5StzaSBF9nY

- Jhannybean

What I've got so far is that.. |dw:1444608594950:dw|

- Jhannybean

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.

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## More answers

- amistre64

|dw:1444609095726:dw|

- amistre64

\[\int_{0}^{h}xy~dz\]
\[\int_{0}^{h}kn~z^2~dz\]
\[\frac13 kn~h^3~\]
pfft, somethings aloof

- Jhannybean

Ahh... I was approaching this without calculus haha

- amistre64

i spose h=zmax in this case ...
\[\frac{1}{3}(kz)(nz)z=\frac{1}{3}xyz\]
might have a bad change of variable is all

- Jhannybean

How did you find \(x=kz\) and \(y=nz\)? are \(k\) and \(n\) just scaling factors?

- amistre64

to make life simpler i turned the pyramid upside down so that the lines defined would go thru the origin is all

- amistre64

|dw:1444609883979:dw|
allowing k and n to account for any width/depth and z for the height

- amistre64

the volume of any slice being xy dz, or dh for a dummy variable

- Jhannybean

I'll bbs. afking for a moment.

- mathstudent55

Start with a cube.
|dw:1444741611276:dw|

- mathstudent55

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.

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