Figure N7–17This shell’s radius, r, is the distance from the axis to the rectangular strip, and
its height is the height of the rectangular strip, h. When the shell is unwound and
flattened to form a rectangular solid, the length of the solid is the circumference
of the cylinder, 2πr, its height is the height of the cylinder, h, and its thickness is
the thickness of the rectangular strip, Δx. Thus: .
Example 10 __
Find the volume of the solid generated when the region bounded by y = x^2 , x = 2,
and y = 0 is rotated about the line x = 2. See Figure N7–18.
SOLUTION:
About the x = 2.
Shell.
Figure N7–18(Note that we obtained the same result using disks in Example 7.)