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Finding the Volume of a Pyramid or Cone

Date: 05/09/2002 at 21:31:11
From: zach
Subject: for some reason i don't get it

Hi, 

I just don't get how to find the volume of a pyramid or a cone. 
Hope you can help me.


Date: 05/09/2002 at 22:33:01
From: Doctor Peterson
Subject: Re: for some reason i don't get it

Hi, Zach.

Suppose you have a pyramid (I choose a square pyramid just 
because it's easiest to draw, but this is true regardless of the 
shape):

           +
          /|\
         / | \
        /  |  \
        /  |  \
       /   |   \
      /    |    \
      /    |    \
     /     |     \
    +      |      +
        \  |  /
           +

Picture making a prism of the same height on the same base:

           +
        /     \
    +             +
    |   \     /   |
    |      +      |
    |      |      |
    |      |      |
    |      |      |
    |      |      |
    |      |      |
    |      |      |
    +      |      +
        \  |  /
           +

Its volume is the product of the area of its base times the 
height; that's because each 1-unit layer can hold as many 1-unit 
cubes as there are 1-unit squares in the base, and there are h 
layers.

Now, the volume of the pyramid is 1/3 of the volume of this 
prism; and the same is true for a cone compared to a cylinder 
with the same base and height.

So just work out the area of the base, by whatever formula you 
need, and multiply by the height; then divide by 3 to get the 
volume of the pyramid or cone.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Higher-Dimensional Geometry

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