91
Chapter 11: Applications of Integration
684. The base of a solid S is an elliptical region
with the boundary curve 4x
2
+ 9y
2
= 36.
Cross-sectional slices perpendicular to the
y-axis are squares. Find the volume of the
solid.
685. The base of a solid S is triangular with
vertices at (0, 0), (2, 0), and (0, 4). Crosssectional slices perpendicular to the y-axis
are isosceles triangles with height equal to
the base. Find the volume of the solid.
686. The base of a solid S is an elliptical region
with the boundary curve 4x
2
+ 9y
2
= 36.
Cross-sectional slices perpendicular to the
x-axis are isosceles right triangles with the
hypotenuse as the base. Find the volume
of the solid.
687. The base of a solid S is triangular with
vertices at (0, 0), (2, 0), and (0, 4).
Cross-sectional slices perpendicular to the
y-axis are semicircles. Find the volume of
the solid.
679. The region is bounded by y = sec x, y = 0,
and 0
3
≤ ≤
x π and is rotated about the
line y = 4.
680. The region is bounded by the curves x = y
2
and x = 4 and is rotated about the line x = 5.
681. The region is bounded by the curves y = e
–x
,
y = 0, x = 0, and x = 1 and is rotated about
the line y = –1.
Finding Volume Using
Cross-Sectional Slices
682–687 Find the volume of the indicated region
using the method of cross-sectional slices.
682. The base of a solid C is a circular disk that
has a radius of 4 and is centered at the
origin. Cross-sectional slices perpendicular
to the x-axis are squares. Find the volume
of the solid.
683. The base of a solid C is a circular disk that
has a radius of 4 and is centered at the
origin. Cross-sectional slices perpendicular
to the x-axis are equilateral triangles. Find
the volume of the solid.