Chapter 7 Integration 15 Set And Evaluate The

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416 Chapter 7: Applications of Integration
7.4 Arc Length and Surfaces of Revolution
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the arc length of the graph of the function over the interval [14,
16].
a.
b.
c.
d.
e.
____ 2. Find the arc length of the graph of the function over the interval [0,6].
a.
b.
c.
d.
e.
____ 3. Find the arc length of the graph of the function over the interval [1,2].
a.
b.
c.
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7.4 Arc Length and Surfaces of Revolution 417
d.
e.
____ 4. Find the arc length of the graph of the function over the interval
[1,64].
a.
b.
c.
d.
e.
____ 5. Find the arc length of the graph of the function over the interval
.
a.
b.
c.
d.
e.
____ 6. Find the arc length of the graph of the function over the interval
.
a.
b.
c.
d.
e.
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418 Chapter 7: Applications of Integration
____ 7. Use the integration capabilities of a graphing utility to approximate the arc length of
the graph of on the interval . Round your answer to three decimal places.
a. 3.620
b. 5.020
c. 10.540
d. 3.820
e. 5.270
____ 8. Electrical wires suspended between two towers form a catenary modeled by the
equation where x and y are measured in meters. The towers are 50
meters apart. Find the length of the suspended cable. Round your answer to three decimal places.
a. 94.421m
b. 50.000 m
c. 64.077 m
d. 40.048 m
e. 47.211 m
____ 9. A barn is 75 feet long and 50 feet wide. A cross section of the roof is the inverted
catenary . Find the number of square feet of roofing on the barn. Round
your answer to the nearest integer.
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7.4 Arc Length and Surfaces of Revolution 419
a. 4180 square feet
b. 4200 square feet
c. 2100 square feet
d. 1875 square feet
e. 3750 square feet
____ 10. Find the arc length from clockwise to (2,
23
) along the circle .
Round your answer to four decimal places.
a. 4.1888
b. 0.2618
c. 0.1309
d. 1.8546
e. 2.0944
____ 11. Find the area of the surface generated by revolving the curve about the x-axis.
.
a.
b.
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420 Chapter 7: Applications of Integration
c.
d.
e.
____ 12. Find the area of the surface generated by revolving the curve about the x-axis.
.
a.
b.
c.
d.
e.
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7.4 Arc Length and Surfaces of Revolution 421
____ 13. Set up and evaluate the definite integral for the area of the surface formed by
revolving the graph of about the x-axis.
a.
b.
c.
d.
e.
____ 14. Find the area of the surface generated by revolving the curve about the y-axis.
a.
b.
c.
d.
e.
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422 Chapter 7: Applications of Integration
____ 15. Set up and evaluate the definite integral for the area of the surface formed by
revolving the graph of about the y-axis. Round your answer to three decimal places.
a. 58.659
b. 117.319
c. 235.685
d. 5.323
e. 2.661
____ 16. Find the area of the surface generated by revolving the curve about the y-axis.
.
a.
b.
c.
d.
e.
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7.4 Arc Length and Surfaces of Revolution 423
____ 17. An ornamental light bulb is designed by revolving the graph of about
the x-axis where x and y are measured in feet. Approximate the amount of glass needed to make the
bulb. (Assume that the glass is 0.016 inches thick.) Round your answer to four decimal places.
a.
b.
c.
d.
e.
____ 18. A bridge has a main span of about 1400 meters. Each of its towers has a height of
about 146 meters. Approximate the length of a parabolic cable along the main span if the length C of
the cable is given by . Round your answer to one decimal place.
a. 719.8 meters
b. 759.4 meters
c. 2120.7 meters
d. 1439.6 meters
e. 2879.2 meters
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424 Chapter 7: Applications of Integration
7.4 Arc Length and Surfaces of Revolution
Answer Section

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