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