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Cylinder Cylinder Shell

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Presentation on theme: "Cylinder Cylinder Shell"— Presentation transcript:

1 Cylinder Cylinder Shell
VOLUMES BY CYLINDRICAL SHELLS Cylinder Cylinder Shell

2 VOLUMES BY CYLINDRICAL SHELLS

3 E-II T-061 VOLUMES BY CYLINDRICAL SHELLS step1 step2 step3 step4 step4
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

4 VOLUMES T-141

5 T-122 VOLUMES BY CYLINDRICAL SHELLS 1 2 3 4 5 6
Graph and Identify the region Draw a line parallel to the rotating line at the point y 2 3 Rotate this line about the rotating line 4 Find: in terms of 5 Find: 6 The volume is given by Note: rotating line is x-axis  dy and we draw a parallel line to x-axis

6 VOLUMES BY CYLINDRICAL SHELLS

7 VOLUMES SUMMARY: The solids in all previous examples are all called solids of revolution because they are obtained by revolving a region about a line. DISK SHELLS WASHER Rotated by x-axis or a line parallel to x-axis Rotated by y-axis or a line parallel to y-axis

8

9 Final T-131

10 VOLUMES T-102

11 VOLUMES T-131


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