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868 Chapter 14: Multiple Integration
14.6 Triple Integrals and Applications
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the following iterated integral.
a.
b.
c.
d.
e.
____ 2. Evaluate the following iterated integral.
a.
b.
c.
d.
e.
____ 3. Evaluate the iterated integral .
a.
b.
c.
14.6 Triple Integrals and Applications 869
d.
e.
____ 4. Set up a triple integral for the volume of the solid bounded by the coordinate planes
and the plane given below.
a.
b.
c.
d.
e.
870 Chapter 14: Multiple Integration
____ 5. Set up a triple integral for the volume of the solid bounded by and
.
a.
b.
c.
d.
e.
14.6 Triple Integrals and Applications 871
____ 6. Set up a triple integral for the volume of the solid bounded above by the cylinder
and below by the paraboloid .
a.
b.
c.
d.
e.
872 Chapter 14: Multiple Integration
____ 7. Use a triple integral to find the volume of the solid shown below.
a.
b.
c.
d.
e.
14.6 Triple Integrals and Applications 873
____ 8. Use a triple integral to find the volume of the solid shown below.
a.
b.
c.
d.
e.
____ 9. Use a triple integral to find the volume of the solid bounded by the graphs of the
equations .
a.
b.
c.
d.
e.
874 Chapter 14: Multiple Integration
____ 10. Rewrite the iterated integral using the order .
a.
b.
c.
d.
e.
14.6 Triple Integrals and Applications 875
____ 11. Sketch the solid whose volume is given by the iterated integral given below and use
the sketch to rewrite the integral using the indicated order of integration.
Rewrite the integral using the order .
a.
b.
c.
d.
e.
876 Chapter 14: Multiple Integration
____ 12. Find of the center of mass of the solid of given density bounded by
the graphs of the equations .
a.
b.
c.
d.
e.
____ 13. Find the centroid of the solid region bounded by the graphs of the equations. Use a
computer algebra system to evaluate the triple integral. (Assume uniform density and find the center
of mass.)
a.
b.
c.
d.
e.
____ 14. Find for the indicated solid with density function .
a.
b.
14.6 Triple Integrals and Applications 877
c.
d.
e.
____ 15. Set up a triple integral that gives the moment of inertia about the -axis of the solid
region Q of density given below.
a.
b.
c.
d.
e.
878 Chapter 14: Multiple Integration
____ 16. Find the center of mass of the solid bounded by and with
density function .
a.
b.
c.
d.
e.
____ 17. Find the average value of over the region Q, where Q is a
cube in the first octant bounded by the coordinate planes, and the planes and . The
average value of a continuous function over a solid region Q is , where
V is the volume of the solid region Q.
a.
b.
c.
d.
e.
14.6 Triple Integrals and Applications 879
____ 18. Find the average value of over the region Q, where Q is a
tetrahedron in the first octant with vertices and . The average
value of a continuous function over a solid region Q is , where V is
the volume of the solid region Q.
a.
b.
c.
d.
e.
880 Chapter 14: Multiple Integration
14.6 Triple Integrals and Applications
Answer Section
MULTIPLE CHOICE
