Figure N7–16See Questions 19, 21, 48, 50, and 54 in the Practice Exercises for examples in
which washers are regarded as the differences of two disks.
Occasionally when more than one method is satisfactory we try to use the
most efficient. In the answers to each question in the Practice Exercises, a sketch
is shown and the type and volume of a typical element are given. The required
volume is then found by letting the number of elements become infinite and
applying the Fundamental Theorem.
SHELLS‡
A cylindrical shell may be regarded as the outer skin of a cylinder. Its volume is
the volume of the rectangular solid formed when this skin is peeled from the
cylinder and flattened out. As an example, consider the volume of the solid of
revolution formed when the region bounded by the two curves seen in Figure
N7–17 is revolved around the y-axis. We think of the rectangular strip of the
region at the left as generating the shell, ΔV (an element of the volume), shown
at the right.