VOLUMES BY CYLINDRICAL SHELLS Cylinder Shell VOLUMES BY
VOLUMES BY CYLINDRICAL SHELLS Cylinder Shell
VOLUMES BY CYLINDRICAL SHELLS Example: Find the volume of the solid obtained by rotating the region enclosed by the curves y=sin(x) and y=0 about the y-axis. Find the volume of the resulting solid. Disk Method The method of shells is fundamentally different from the method of disks. The method of disks involves slicing the solid perpendicular to the axis of revolution to obtain the disks. However, the method of shells fills the solid with cylindrical shells Shell Method This demo was developed by Lila F. Roberts College of Information & Mathematical Sciences Clayton State University Morrow, GA 30260
VOLUMES BY CYLINDRICAL SHELLS
VOLUMES BY CYLINDRICAL SHELLS The volume is given by Find the surface area
VOLUMES BY CYLINDRICAL SHELLS step 1 step 2 Graph and Identify the region Draw a line parallel to the rotating line at the point x step 3 Rotate this line about the rotating line step 4 Find: in terms of step 5 The volume is given by Note: rotating line is y-axis dx and we draw a parallel line to y-axis
VOLUMES BY CYLINDRICAL SHELLS
VOLUMES BY CYLINDRICAL SHELLS T-122
VOLUMES T-102
VOLUMES BY CYLINDRICAL SHELLS
VOLUMES BY CYLINDRICAL SHELLS rotating line Parallel to y-axis The volume is given by CYLINDRICAL SHELLS Find the surface area rotating line Parallel to x-axis The volume is given by Find the surface area
VOLUMES BY CYLINDRICAL SHELLS Remarks rotating line Parallel to x-axis CYLINDRICAL SHELLS (6. 2) Remarks DESK(6. 1) Cross-section is DISK rotating line Parallel to y-axis rotating line Parallel to x-axis rotating line Parallel to y-axis Cross—section is WASHER SHELL Method
VOLUMES BY CYLINDRICAL SHELLS T-131
VOLUMES T-072
T-111
VOLUMES BY CYLINDRICAL SHELLS T-111
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