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14.7 Triple Integrals in Other Coordinates 881
14.7 Triple Integrals in Other Coordinates
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.
882 Chapter 14: Multiple Integration
___ 3. Evaluate the iterated integral .
a.
b.
c.
d.
e.
____ 4. Evaluate the following iterated integral.
a.
224
3
b.
224
3
c.
288
7
d.
40
e.
288
7
14.7 Triple Integrals in Other Coordinates 883
____ 5. Convert the integral below from rectangular coordinates to both cylindrical and
spherical coordinates, and evaluate the simpler iterated integral.
a.
b.
c.
d.
e.
____ 6. Convert the integral below from rectangular coordinates to both cylindrical and
spherical coordinates, and evaluate the simpler iterated integral.
a.
b.
c.
d.
e.
884 Chapter 14: Multiple Integration
____ 7. Use cylindrical coordinates to find the volume of the solid inside both
and .
a.
b.
c.
d.
e.
____ 8. Use cylindrical coordinates to find the volume of the solid bounded above by
and below by .
a.
b.
c.
d.
e.
14.7 Triple Integrals in Other Coordinates 885
____ 9. Use cylindrical coordinates to find the volume of the solid inside the sphere
and above the upper nappe of the cone .
a.
b.
c.
d.
e.
____ 10. Use cylindrical coordinates to find the mass of the solid
where .
a.
b.
c.
d.
e.
886 Chapter 14: Multiple Integration
____ 11. Use cylindrical coordinates to find the volume of the cone where
and .
a.
b.
c.
d.
e.
____ 12. Use spherical coordinates to find the volume of the solid inside
and outside , and above the xy-plane.
a.
b.
c.
d.
e.
14.7 Triple Integrals in Other Coordinates 887
____ 13. Use spherical coordinates to find the volume of the solid inside the torus given by
.
a.
b.
c.
d.
e.
____ 14. Use spherical coordinates to find the volume of the solid between the spheres
and and inside the cone .
a.
b.
c.
d.
e.
____ 15. Use spherical coordinates to find the mass of the sphere with the
given density. The density at any point is proportional to the distance of the point from the z-axis.
a.
b.
c.
d.
e.
888 Chapter 14: Multiple Integration
____ 16. Use spherical coordinates to find the z coordinate of the center of mass of the solid
lying between two concentric hemispheres of radii 4 and 7, and having uniform density k.
a.
b.
c.
d.
e.
____ 17. Use spherical coordinates to find the z coordinate of the center of mass of the solid
lying between two concentric hemispheres of radii 6 and 7, and having uniform density k.
a.
b.
c.
d.
e.
14.7 Triple Integrals in Other Coordinates 889
14.7 Triple Integrals in Other Coordinates
Answer Section
MULTIPLE CHOICE
