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Q&A #771


Formula for volume of cones/pyramids

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 12, 1998 at 17:12:51
Subject: Re: Formula for volume of cones/pyramids

Hi, Dean,

For many students, seeing is believing.

Try to find a clear cylinder that you can fill with rice or some other small
dry commodity such as dried green peas.

Make a cone to fit inside the cylinder so that the height of the cone is the 
height of the cylinder and the base of the cone fits the base of the 
cylinder.   You can do this out of a sheet of paper where you have cut a 
semi-circle whose radius is the distance from the edge of the cylinder to the 
middle of the opposite base.  The sector of the circle can be fitted into the 
cylinder.  Tape the side of the cone so that you can fill it with rice.  Show 
that you have to fill it three times in order to fill the cylinder,

It is possible to cut three triangular based pyramids from one triangular 
based rectangular solids and prove that they all have the same volume.  I 
could not explain this by writing. This visual is in an old 1980's edition 
of Geometry by Houghton Mifflin.

Try the rice method.

-Marielouise, for the Teacher2Teacher service

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