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408 Chapter 7: Applications of Integration
7.3 Volume: The Shell Method
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the shell method to set up and evaluate the integral that gives the
volume of the solid generated by revolving the plane region about the y-axis.
a.
b.
c.
d.
e.
____ 2. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region about the y-axis.
a.
b.
c.
d.
e.
7.3 Volume: The Shell Method 409
____ 3. Use the shell method to set up and evaluate an integral that gives the volume of the
solid generated by revolving the plane region about the y-axis.
a.
b.
c.
d.
e.
____ 4. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region bounded by
about the y-axis. Round your answer to three decimal places.
a. 5.987
b. 0.561
c. 2.047
d. 0.972
e. 2.917
____ 5. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region about the x-axis.
a.
b.
c.
d.
e.
410 Chapter 7: Applications of Integration
____ 6. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region about the x-axis.
a.
b.
c.
d.
e.
____ 7. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region about the x-axis.
a.
b.
c.
d.
e.
7.3 Volume: The Shell Method 411
____ 8. Use the shell method to set up and evaluate the integral that gives the volume of the
solid generated by revolving the plane region bounded by about the x-axis.
a.
b.
c.
d.
e.
____ 9. Use the shell method to find the volume of the solid generated by revolving the plane
region about the line .
a.
b.
c.
d.
e.
____ 10. Use the shell method to find the volume of the solid generated by revolving the plane
region bounded by about the line .
a.
b.
c.
d.
e.
412 Chapter 7: Applications of Integration
____ 11. Use the disk or shell method to find the volume of the solid generated by revolving
the region bounded by the graphs of the equations about the line .
a.
b.
c.
d.
e.
____ 12. Use the disk or the shell method to find the volume of the solid generated by
revolving the region bounded by the graphs of the equations about the x-axis.
a.
b.
c.
d.
e.
____ 13. Use the disk or the shell method to find the volume of the solid generated by
revolving the region bounded by the graphs of the equations about the line
.
a.
b.
c.
d.
e.
7.3 Volume: The Shell Method 413
____ 14. Use the disk or shell method to find the volume of the solid generated by revolving
the region bounded by the graphs of the equations about the line .
a.
b.
c.
d.
e.
____ 15. Use the disk or the shell method to find the volume of the solid generated by
revolving the region bounded by the graphs of the equations about the
x-axis. Round your answer to two decimal places.
a. 674.33
b. 17.75
c. 96.05
d. 301.76
e. 453.96
____ 16. Use the disk or shell method to find the volume of the solid generated by revolving
the region in the first quadrant bounded by the graph of the equation about the given line.
(i) the x-axis; (ii) the y-axis
a.
b.
c.
d.
e.
414 Chapter 7: Applications of Integration
____ 17. A solid is generated by revolving the region bounded by and about
the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth
of the volume is removed. Find the diameter of the hole. Round your answer to three decimal places.
a. 10.733
b. 11.167
c. 4.392
d. 2.536
e. 8.785
____ 18. A solid is generated by revolving the region bounded by and
about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-
third of the volume is removed. Find the diameter of the hole. Round your answer to three decimal
places.
a. 11.547
b. 5.774
c. 4.867
d. 18.838
e. 9.734
7.3 Volume: The Shell Method 415
7.3 Volume: The Shell Method
Answer Section
