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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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