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### Course: Geometry (FL B.E.S.T.)>Unit 9

Lesson 5: Cavalieri's principle and dissection methods

# Volume of pyramids intuition

The volume of a pyramid is a fraction of the volume of the rectangular prism that encloses it. We can find out what that fraction is by cutting a prism into several pyramids. Created by Sal Khan.

## Want to join the conversation?

• How is bro so good at drawing 3d shapes dang
• just better
• At , why do you divide by 2?
• Hi James, Sal divides by 2 because, for that pyramid, the height is half(thus the division by 2) of x, which is the width of the rectangular prism that was constructed for the proof. At the beginning of the video, Sal defined that the volume of a pyramid is k(a constant) times the base area times the height. That is no different with the pink pyramid. Sal just integrates the x/2 into (k*y*z*x)/2, which is the same as k*y*z*(x/2) or k*y*z*1/2*x.
I hope that helped, and sorry for the later reply.
~Hannah
• is it confusing to any one because it is to me
• At , how is V = kxy.z/2 equal to v = kxyz/2 ?
• If you have a set of numbers that is only multiplied/divided, then the order that you multiply/divide doesn't matter. You could have kxy * (z/2) or (kxy*z)/2.

• Why would we multiply xyz by another constant?
• At around , Sal says that if you just had the formula be V = xyz without any constant, it simply gives you the volume of a rectangular prism with those dimensions. We're looking for the volume of a pyramid, so we have to do something to the formula, namely multiply it by 1/3.
• At , Sal writes xyz/2. Isn't it only z that's divided by 2? Does k get divided by 2 as well?
• Do not think that you are dividing each of the terms by 2, you are only dividing the product of all the terms by 2, so yes you could also include k in the numerator.
Simple example: 2 * 7 * 6/4 would give the same answer as (2 * 7 * 6)/4.
• At , why did it have to be multiplied by some constant (k)?
I did not really understand his intuitive sense behind that.
Thanks in advance and have a BLESSED day!
• Is the formula and intuition behind it the same for triangular pyramids, etc.?