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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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