Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

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Presentation transcript:

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS Area of the surface

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS The volume is given by Find the surface area

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

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS Term111 1 2 3

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

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS Term111 1 2 3

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

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

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

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS

Sec 6.3: VOLUMES BY CYLINDRICAL SHELLS