1. Volumes by Slicing
7.3
Solids of Revolution

2. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

3. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

4. Find the volume of the solid generated by revolving the regions
bounded by
about the y-axis.

5. Find the volume of the solid generated by revolving the regions
bounded by
about the x-axis.

6. Find the volume of the solid generated by revolving the regions
bounded by
about the line y = -1.

7. NO CALCULATOR
Let R be the first quadrant region enclosed by the graph of
a) Find the area of R in terms of k.
Find the volume of the solid generated when R is
rotated about the x-axis in terms of k.
c) What is the volume in part (b) as k approaches infinity?

8. Let R be the first quadrant region enclosed by the graph of
a) Find the area of R in terms of k.

9. Let R be the first quadrant region enclosed by the graph of
Find the volume of the solid generated when R is
rotated about the x-axis in terms of k.

10. Let R be the first quadrant region enclosed by the graph of
c) What is the volume in part (b) as k approaches infinity?

11. CALCULATOR REQUIRED
Let R be the region in the first quadrant under the graph of
a) Find the area of R.
The line x = k divides the region R into two regions. If the
part of region R to the left of the line is 5/12 of the area of
the whole region R, what is the value of k?
Find 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.

12. Let R be the region in the first quadrant under the graph of
a) Find the area of R.

13. Let R be the region in the first quadrant under the graph of
The line x = k divides the region R into two regions. If the
part of region R to the left of the line is 5/12 of the area of
the whole region R, what is the value of k? A

14. Let R be the region in the first quadrant under the graph of
Find 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.
Cross Sections

15. 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. Find the volume of the
solid in terms of a. (NO PI)

16. CALCULATOR REQUIRED

17. 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.

18. 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.

19. 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 closest to
a) b) c) d) e) 2.91

20. 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

21. CALCULATOR REQUIRED

22. NO CALCULATOR

23. CALCULATOR REQUIRED

24. NO CALCULATOR

25. CALCULATOR REQUIRED

26. CALCULATOR REQUIRED