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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