14.5 Surface Area
888
14.5 Surface Area
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the area of the portion of the surface that lies above the triangular region
with vertices , and .
4
36
18
162
324
____ 2. Find the area of the surface given by over the region R.
R: square with vertices
a.
b.
c.
d.
e.
____ 3. Find the area of the surface given by over the region R.
R: square with vertices
a.
b.
c.
889 Chapter 14: Multiple Integration
d.
e.
____ 4. Find the area of the portion of the surface that lies above the region
.
72
36
____ 5. Find the area of the surface given by over the region R.
R: rectangle with vertices
a.
b.
c.
d.
e.
14.5 Surface Area
890
____
6.
Find the area of the portion of the surface
that lies above the
region
a.
0.05
b.
2.18
c.
11.97
d.
1.22
e.
12.51
____
7.
Find the area of the portion of the surface
that lies above the
region
. Round your answer to two decimal places.
9.29
18.58
69.20
5.33
0.65
____ 8. Find the area of the surface given by over the region R.
a.
b.
c.
d.
e.
891
Chapter 14: Multiple Integration
____
9.
Find the area of the portion of the surface
that lies above
the region
. Round your answer to two decimal places.
144.00
118.44
904.78
452.39
1,421.22
____ 10. Find the area of the surface of the portion of the plane
in the first octant.
a.
b.
c.
d.
e.
____ 11. Find the area of the surface for the portion of the paraboloid in the
first
octant.
a.
b.
c.
14.5 Surface Area
892
d.
e.
____
12.
Find the area of the surface for the portion of the sphere
inside
the cylinder
.
a.
b.
c.
d.
e.
____
13.
Write a double integral that represents the surface area of
over
the region R: triangle with vertices
. Use a computer algebra system to evaluate
the double integral. Round your answer to two decimal places.
a.
b.
c.
d.
e.
____ 14.
Write a double integral that represents the surface area of
over the region R:
. Use a computer algebra system to evaluate the
double integral. Round your answer to four decimal places.
a.
b.
c.
d.
e.
893
Chapter 14: Multiple Integration
____
15.
Set up a double integral that gives the area of the surface of the graph of f over the
region R.
a.
b.
c.
d.
e.
____ 16. Set up a double integral that gives the area of the surface on the graph of
over the region .
a.
14.5 Surface Area
894
b.
c.
d.
e.
____ 17. Set up a double integral that gives the area of the surface of the graph of f over the
region R.
a.
b.
895 Chapter 14: Multiple Integration
c.
d.
e.
____ 18. A company produces a spherical object of radius 17 centimeters. A hole of radius 7
centimeters is drilled through the center of the object. Find the volume of the object.
a.
b.
c.
d.
e.
____ 19. A company produces a spherical object of radius 24 centimeters. A hole of radius 5
centimeters is drilled through the center of the object. Find the outer surface area of the object.
cm3
cm3
cm3
cm3
cm3
14.5 Surface Area 896
14.5 Surface Area
Answer Section
897 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
898
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.
899
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
900
____ 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.
901 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
902
____ 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.
903
Chapter 14: Multiple Integration
____
10.
Rewrite the iterated integral
using the order
.
a.
b.
c.
d.
e.
14.6 Triple Integrals and Applications
904
____ 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.
905
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.
14.6 Triple Integrals and Applications
906
b.
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.
907
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.