1 / 17

Solids of Revolution

What will happen if a right triangle is revolved about a side, like the one below?. Solids of Revolution. -- formed when a region in a plane is revolved about a line. -- the line is called the axis of revolution. y. x. 0. Activities. Winplot can help you visualise the revolution

valtina-tony
Download Presentation

Solids of Revolution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. What will happen if a right triangle is revolved about a side, like the one below? Solids of Revolution -- formed when a region in a plane is revolved about a line -- the line is called the axis of revolution

  2. y x 0

  3. Activities • Winplot can help you visualise the revolution • Follow the instructions given on your worksheet • Write down your observations on the space provided Go! READY?

  4. Examples

  5. An interesting solid Can you tell any difference of this solid from the previous shown solids?

  6. How to find the volume of solid of revolution? Suggest methods for finding volume of an unknown solid. Recall some known solids that we know how to find the volume

  7. Use Winplot to view the solid in different ways, is the cross section a known figure to you? Yes. What is the figure? The figure is a circle. What can we do to the unknown solid? We can cut the solid into slices.

  8. Activities • JkGraph can help you visualise how the solid is cut into slices • Follow the instructions given on your worksheet • Write down your observations on the space provided Go! READY?

  9. y = f(x)

  10. Volume of the disk: xi y = f(x) f(xi) xi

  11. The volume of the whole solid is found by adding the volume of disks together. y = f(x) Definite Integration can help to do the addition. a b

  12. y y = sin x 1  0 x An example: The area bounded by the curve y = sin x and the x-axis between x = 0 to x =  is revolved about the x-axis. Find the volume of the solid of revolution.

More Related