182
Fig. 22-24
(b) Interchange a and b in (a):
Fig. 22-25
Fig. 22-26
22.49
Find the volume of the solid obtained by rotating about the Jt-axis the region in the first quadrant under the line
segment from (0, rj to (h, r 2 ), where 0 of a frustum of a cone with height h and radii r l and r 2 of the bases.)
The equation of the line is
By the disk formula,
(a) We double the value obtained from the disk formula applied to the part of the region in the first quadrant
(see Fig. 22-25):
22.48
Find the volume of the ellipsoid obtained when the ellipse
about the y-axis.
is rotated (a) about the *-axis, (b)
22.47
Same as Problem 22.46, but with the rotation around the y-axis.
Use the cylindrical shell formula:
The disk formula applies:
Note that this approaches TT as
22.46
Find the volume of the solid generated when the region in the first quadrant under the hyperbola xy = 1,
between x = 1 and x = b>l, is rotated about the *-axis.
22.45
Same as Problem 22.44, but the rotation is about the y-axis.
Use the cylindrical shell formula:
Use the disk formula:
22.44
Calculate the volume of the solid paraboloid generated when the region in the first quadrant under the parabola
x = y". between x = 0 and x = b, is rotated about the *-axis.
CHAPTER 22