Pre-Algebra: Volume of a Cylinder
by Thinkwell
Free
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About this Lesson
- Type: Video Tutorial
- Length: 1:51
- Media: Video/mp4
- Posted: 01/28/2009
- Use: Watch Online & Download
- Download: MP4 (iPod compatible)
- Size: 21 MB
This lesson is part of the series: Pre-Algebra Review
To find the volume for a cylinder, you will use the same volume formula that you would use to calculate the volume of a rectangular prism, V=Bh. However, for a cylinder, the area of the base, B, is equal to Pi * r^2, where r is the radius of the base. This is because the base is circular in shape, and the area of a circle is equal to pi*r^2 whereas the area of a rectangle (the shape of the base of a rectangular prism) is equal to length*width.
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
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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 CYLINDER
All right, let’s take a look at a geometric application together. A can of soup is shaped like a cylinder. Let’s find the volume to the nearest tenth. In case we have to pull out pi, we are going to use 3.14 for that approximation to that value pi. Here is our can of soup, which looks like a cylinder. That is good. We want to now find the volume. We can use the same principles we developed with the prisms to find the volume of a cylinder. Namely, all we are going to do is to find the area of the base and multiply it by the height. The volume will be the area of the base, which will be the area of a circle, pi r squared. Pi times, in this case the radius is 3 inches, so it will be 3 squared, which is 9. That is the base, and we multiply that by the height, which is 5. We see 9 times 5 is 45. 45 pi is the exact answer to the volume. What is the volume of this can? 45 pi.
If you want to give a numerical approximation and round, then we can use a calculator and multiply 45 by our approximated 3.14. We get 141.3 after we round. What are our units? Our units are going to be inches squared on the top by inches, so inches cubed – always inches cubed for volume in three dimensions. So 141.3 inches cubed is the volume of this can of soup.
Next time you look at a can of soup, you can think that its contents describe its volume, and you can find the formula. I will see you soon.
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