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Pre-Algebra: Volume of a Pyramid

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About this Lesson

  • Type: Video Tutorial
  • Length: 2:01
  • Media: Video/mp4
  • Posted: 01/28/2009
  • Use: Watch Online & Download
  • Download: MP4 (iPod compatible)
  • Size: 29 MB

This lesson is part of the series: Pre-Algebra Review

It appears that finding the volume of a pyramid would be tricky, but Professor Burger teaches a simple formula, V=(1/3)Bh. The height, h, in the case of a pyramid, is in the very center of the pyramid, from the peak to the base. B is equal to the area of the base of the pyramid. This formula is similar to the formula used to calculate the volume of a rectangular prism (V=Bh, where B is the area of the base and h is the height of the prism) or cylinder (also V=Bh, where B is the area of the base and h is the height of the cylinder).

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

Thinkwell
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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

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VOLUME OF A PYRAMID

Suppose we want to find the volume of this rectangular pyramid. Well, it seems like a complicated object, but it turns out that the formula for the volume is really simple. I want to share it with you, so you can enjoy it with me. It turns out the volume is one-third the area of the base times the height. You compute the area of the base and multiply it by the height. The way you find the height is you imagine taking a piece of sting and putting it at the very top of the peek, so at this vertex right here. Put a weight at the end of the string, and let the string fall down. It will hit the floor at a perpendicular angle, so sort of perpendicular to the floor. It’s that perpendicular length that you want. That represents the height. You find the area of the base.

For example, if we have a rectangular base, it will be length times width to compute the area of the base. If it were a different shaped base, then, of course, the area of the base would be a different formulation. For this example we have this. So, what would it be? It would be one-third, one-third, you heard me. Length times width, which is 3 times 4 times the height. We can simplify this a little bit because 3 divided by 3 simplifies to just 1. We are left with 4 times 10, so the volume of this particular pyramid is 40. What are my units? They are centimeters cubed. Centimeters cubed represent the units. So, the volume of a pyramid is no big deal. You just find the area of the base multiplied by the height multiplied by one-third.

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