1 / 12

Volumes

Volumes. Right Cylinder. Volume of a Right Cylinder (Slices). Cross section is a right circular cylinder with volume . Also obtained as a solid of revolution. Consider the case when h=5 and r=2. Volume of a Rectangular Box. Area of a cross section is b*l.

carr
Download Presentation

Volumes

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. Volumes

  2. Right Cylinder

  3. Volume of a Right Cylinder (Slices) Cross section is a right circular cylinder with volume Also obtained as a solid of revolution Consider the case when h=5 and r=2

  4. Volume of a Rectangular Box Area of a cross section is b*l Cross section is a right cylinder with volume Consider the case of a box with dimensions 3x5x7

  5. Volume of a Sphere of radius r (slices) Cross section is a right cylinder with volume Consider the case of a sphere of radius r=3

  6. Another Example Sketch the solid of revolution obtained by rotating around x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=5 and find its volume

  7. Volume using Shells

  8. Example Sketch the solid of revolution obtained by rotating about x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=1.2 and find its volume

  9. Cylindrical Shells • Definition of a shell • Animations

  10. Formulas • Shell in general position Volume of shell

  11. Volume Formulas Function y=f(x) • Rotating about y-axis • Function x=f(y) • Rotating about x-axis

More Related