398 Chapter 7: Applications of Integration
7.2 Volume: The Disk Method
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Set up and evaluate the integral that gives the volume of the solid formed by
revolving the region bounded by and about the -axis.
a.
b.
c.
d.
e.
____ 2. Set up and evaluate the integral that gives the volume of the solid formed by
revolving the region bounded by and in the first quadrant about the -axis.
a.
b.
7.2 Volume: The Disk Method 399
c.
d.
e.
____ 3. Set up and evaluate the integral that gives the volume of the solid formed by
revolving the region bounded by , and about the -axis.
a.
b.
c.
d.
e.
____ 4. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations , and about the line .
a.
448
3
b.
4, 480
3
400 Chapter 7: Applications of Integration
c.
448
3
d.
4, 480
3
e.
4, 840
3
____ 5. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations , and about the line .
a.
16
3
b.
8
3
c.
16
3
d.
32
3
e.
32
3
____ 6. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the given lines.
a.
b.
c.
7.2 Volume: The Disk Method 401
d.
e.
____ 7. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the given lines.
a.
b.
c.
d.
e.
____ 8. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the given lines.
a.
b.
c.
402 Chapter 7: Applications of Integration
d.
e.
____ 9. 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.
____ 10. 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.
7.2 Volume: The Disk Method 403
____ 11. 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. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the -axis.
a.
b.
c.
d.
e.
404 Chapter 7: Applications of Integration
____ 13. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the -axis.
a.
b.
c.
d.
e.
____ 14. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the -axis. Verify your results using the integration capabilities of a
graphing utility.
a.
b.
c.
d.
e.
7.2 Volume: The Disk Method 405
____ 15. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations , and about the -axis. Round your
answer to four decimal places.
a. 5.3098
b. 12.2824
c. 20.6444
d. 15.9387
e. 37.9232
____ 16. A tank on the wing of a jet aircraft is formed by revolving the region bounded by the
graph of and the x-axis about the x-axis, where x and y are measured in
meters. Find the volume of the tank. Round your answer to two decimal places.
a. 0.45 m3
b. 0.33 m3
c. 0.03 m3
d. 1.79 m3
e. 0.12 m3
____ 17. A tank on a water tower is a sphere of radius 65 feet. Determine the depth of the
water when the tank is filled to one-fourth of its total capacity. (Note: Use the zero or root feature of a
graphing utility after evaluating the definite integral.) Round your answer to two decimal places.
a. 20.66 feet
b. 54.63 feet
c. 34.67 feet
d. 42.43 feet
e. 10.36 feet
406 Chapter 7: Applications of Integration
7.2 Volume: The Disk Method
Answer Section
7.2 Volume: The Disk Method 407