1 / 10

7.3 Volumes With Known Cross Sections

7.3 Volumes With Known Cross Sections. Volumes with Known Cross Sections. A solid has as its base the circle x 2 + y 2 = 9 , and all cross sections parallel to the y-axis are squares. Find the volume of the solid. Solids with Known Cross Sections.

wayne
Download Presentation

7.3 Volumes With Known Cross Sections

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. 7.3 Volumes With Known Cross Sections

  2. Volumes with Known Cross Sections • A solid has as its base the circle x2 + y2 = 9, and all cross sections parallel to the y-axis are squares. Find the volume of the solid.

  3. Solids with Known Cross Sections • If A(x) is the area of a cross section of a solid and A(x) is continuous on [a, b], then the volume of the solid from x = a to x = b is

  4. Volumes with Known Cross Sections • A solid has as its base the circle x2 + y2 = 9, and all cross sections parallel to the y-axis are squares. Find the volume of the solid. 3 Area of cross section (square)? -3 y 3 -3 y-coordinate So, s = 2y x dx

  5. Volumes with Known Cross Sections • A solid has as its base the circle x2 + y2 = 9, and all cross sections parallel to the y-axis are squares. Find the volume of the solid. 3 Area of cross section (square)? -3 y Volume of solid: 3 -3 x dx

  6. Volumes with Known Cross Sections • A solid has as its base the circle x2 + y2 = 9, and all cross sections parallel to the y-axis are squares. Find the volume of the solid. Volume of solid: 3 -3 y 3 -3 x dx

  7. Known Cross Sections • Ex: The base of a solid is the region enclosed by the ellipse The cross sections are perpendicular to the x-axis and are isosceles right triangles whose hypotenuses are on the ellipse. Find the volume of the solid. 5 -2 a a 2 -5

  8. 1.) Find the area of the cross section A(x). y 2.) Set up & evaluate the integral. 5 -2 a a 2 -5

  9. Example • The base of a solid is the region enclosed by the triangle whose vertices are (0, 0), (4, 0), and (0, 2). The cross sections are semicircles perpendicular to the x-axis. Find the volume of the solid. y Area of cross section (semicircle)? 2 r is half of the y-value on the line 4 x

  10. Example • The base of a solid is the region enclosed by the triangle whose vertices are (0, 0), (4, 0), and (0, 2). The cross sections are semicircles perpendicular to the x-axis. Find the volume of the solid. y Area of cross section (semicircle)? 2 Volume 4 x (fInt) V = 2.094

More Related