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Pre-Algebra: Surface Area of a Cylinder

by Thinkwell

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About this Lesson

  • Type: Video Tutorial
  • Length: 2:48
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 29 MB
  • Posted: 01/28/2009

This lesson is part of the following series:

Pre-Algebra Review (31 lessons, $61.38)

To find the surface area of a cylinder, you will need to add the surface area of the base, top, and curved surface. The area of both the base and the top will each be Pi * r^2 (the formula for the area of a circle). The area of the curved surface will be the height multiplied by the circumference of the base, 2*Pi*r. The equation for the Surface area is S=(2*Pi*r^2) + (2*Pi*r*h).

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/.

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

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Recent Reviews

Nopic_tan
Ugh, surface area!
06/01/2009
~ brittanie

This video is a great visual resource to find the surface area of a cylinder! It's a much better way to learn surface area than from my teacher's textbook.

Nopic_tan
Ugh, surface area!
06/01/2009
~ brittanie

This video is a great visual resource to find the surface area of a cylinder! It's a much better way to learn surface area than from my teacher's textbook.

SURFACE AREA OF A CYLINDER

If you were to look at the net of a cylinder, so imagine a cylinder where you have a nice can. If you were to cut the top of the can open, cut the can bottom open, and make an incision right along the side of the can and unfold it, that net would look just like this. This would be the side of the round can. These are the bases. The question is: how would you find the surface area of this particular can?

What you would do is you would find the area of the 2 bases, which, notice, is just the area of a circle multiplied by 2. Then you find the area around, which is really just a rectangle. The height of the rectangle is given by the cylinder. The base of the rectangle has area. Let’s think about it. That base has to wrap around that circle once, so it will be the circumference. In fact, it is the circumference times the height. So if you want the formula for the surface area of a cylinder, it is pi r-squared, the area of base times 2, because there is a top and a bottom, plus the area of this rectangle which is the base (the circumference – 2 pi r, remember the circumference is 2 pi r which is this) times the height. This gives us the formula for surface area of a cylinder.

What would it be? The area of this circle is going to be pi r-squared, which will be 25 pi. The area of this circle is the same, 25 pi. What is the circumference of the circle? It will be 10 pi, so this length right here, from here to here, is 10 pi. The total area is going to be 10 pi times 8.1, which 81 pi. What is the total surface area? We add these up. So 25 pi plus 25 pi is 50 pi. 50 pi plus 81 pi is 131 pi. If you want to approximate that, for example, just think of it numerically by approximating by 3.14. We would see that this value comes out to be about 411.34. What are my units? This is area so it will be centimeters squared. Centimeters squared are going to represent the surface area. You can see that just by creating the net associated with a cylinder, we see a long rectangle, two circles, and the circumference of each circle makes up one of the sides of the rectangle. Cool.

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