Download presentation
Presentation is loading. Please wait.
1
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
Area of the surface
2
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
3
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
4
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
The volume is given by Find the surface area
5
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
step1 Graph and Identify the region Draw a line parallel to the rotating line at the point x step2 step3 Rotate this line about the rotating line step4 Find: in terms of step4 Find: step5 The volume is given by Note: rotating line is y-axis dx and we draw a parallel line to y-axis
6
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
7
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
Term111 1 2 3
8
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
rotating line Parallel to y-axis CYLINDRICAL SHELLS (6.3) The volume is given by Find the surface area rotating line Parallel to x-axis CYLINDRICAL SHELLS (6.3) The volume is given by Find the surface area
9
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
Term111 1 2 3
10
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
11
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
12
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
Remarks rotating line Parallel to x-axis CYLINDRICAL SHELLS (6.3) rotating line Parallel to y-axis Remarks rotating line Parallel to x-axis DESK(6.2) rotating line Parallel to y-axis
13
EXAM (is not multiple choice)
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS EXAM (is not multiple choice) Do the graph 1 2 Find intersection points (if needed) 3 Draw a parallel line 4 Find r and h in terms of x 5 Write the formula with a and b 6 Write the volume as an integral More Examples can be found here
14
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
15
Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.