Finding the Volume of a Pyramid or ConeDate: 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/ |
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