Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the arc length of the graph of the function  over the
interval [14, 16].
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2.
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Find the arc length of the graph of the function  over the interval [0,6].
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3.
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Find the arc length of the graph of the function  over the
interval [1,2].
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4.
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Find the arc length of the graph of the function  over the
interval [1,64].
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5.
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Find the arc length of the graph of the function  over the
interval  .
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6.
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Find the arc length of the graph of the function  over the interval  .
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7.
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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 |
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8.
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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 |
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9.
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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.  a. | 4180 square feet | b. | 4200 square feet | c. | 2100 square
feet | d. | 1875 square feet | e. | 3750 square
feet |
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10.
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Find the arc length from  clockwise to (2,  ) 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 |
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11.
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Find the area of the surface generated by revolving
the curve about the x-axis.
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12.
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Find the area of the surface generated by revolving the curve about the
x-axis.  .
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13.
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Set up and evaluate the definite integral for the area of the surface formed by
revolving the graph of  about the x-axis.
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14.
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Find the area of the surface generated by revolving the curve about the
y-axis. 
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15.
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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 |
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16.
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Find the area of the surface generated by revolving the curve about the
y-axis.  .
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17.
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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. 
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18.
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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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