Q&A #4046

Teachers' Lounge Discussion: Volume and Surface Area of Cones

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2001081710:53:22
Subject: Volume and Surface Area of Cones

I read your answer to the pyramid problem.  This is a difficult
problem to explain particularly since most schools don't teach solid
geometry nowadays.  

I bought an old solid geometry book from a library sale several years
ago.  And theorem 37 says that the volume of any pyramid equals 1/3
the product of the base and altitude.  Theorem 36 says the same thing
re a triangular pyramid.  The book is, "Solid Geometry" by Smith &
Ulrich. Copyrighted by World Book co. 1957.  Theorem 36 has a proof
which is rather difficult to visualize in three dimensions.  

I suppose theorem 37 could be extended to a pyramid with 100, 1000 or
so many sides that it would be a cone for all practical purposes, just
as a circle is a many sided polygon.

I cut a stick of butter into a cube and tried to make cuts that
demonstrated the 1/3 idea, but I guess my knife was not hot enough to
make a straight cuts through the butter.   

It seems that the educational companies should be able to make a
manipulative that demonstrates the 1/3 concept.  Maybe somebody can
come up with one.  

In the meantime, I recommend that some of the brighter students get a
copy of a Solid Geometry book and see what they are missing.  I
searched EBAY by typing in "solid geometry" and came up with 5 entries
with copyrights ranging from 1923 to 1943.  All of these books are
rather cheaply priced.

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