1. Disks, Washers, and Cross Sections Review

2. Let R be the region in the first quadrant under the graph of
Setup but do not evaluate the integral necessary to compute
the volume of the solid whose base is the region R
and whose cross sections cut by planes perpendicular
to the x-axis are squares.

3. The base of a solid is the circle . Each section of the
solid cut by a plane perpendicular to the x-axis is a square with
one edge in the base of the solid. Setup but doe not evaluate
the integral to find the volume of the solid in terms of a.

4. Let functions f and g be defined by f(x) = x and , where
k is a positive constant
If R is the region between the graphs of f and g on the interval
[1, 3], setup but do not evaluate an integral expression in
terms of k for the volume of the solid generated when R is
rotated about the x-axis.
Setup up but do not evaluate an integral expression in terms
of k for the volume of the solid generated when R is rotated
about the horizontal line y = -2.

5. Let R be the region marked in the first quadrant enclosed by
the y-axis and the graphs of
as shown in the figure below
Setup but do not evaluate the
integral representing the volume
of the solid generated when R
is revolved around the x-axis. R
Setup, but do not evaluate the
integral representing the volume
of the solid whose base is R and
whose cross sections perpendicular
to the x-axis are squares.

6. Setup, but do not evaluate, the integral necessary to find the
volume of the solid formed when the region bounded by
is revolved about the x-axis.

7. Let R be the region in the first quadrant bounded above by the
graph of f(x) = 3 cos x and below by the graph of
Setup, but do not evaluate, an integral expression in terms of
a single variable for the volume of the solid generated when
R is revolved about the x-axis.
Let the base of a solid be the region R. If all cross sections
perpendicular to the x-axis are equilateral triangles, setup,
but do not evaluate, an integral expression of a single
variable for the volume of the solid.

8. The volume of the solid generated by revolving the first quadrant
region bounded by the curve and the lines x = ln 3 and
y = 1 about the x-axis is
a) b) c) d) e) 2.92

9. The base of a solid is a right triangle whose perpendicular sides
have lengths 6 and 4. Each plane section of the solid
perpendicular to the side of length 6 is a semicircle whose
diameter lies in the plane of the triangle. The volume of the solid
in cubic units is:
a) 2pi b) 4pi c) 8pi d) 16pi e) 24pi