تكلم مع الذكاء الاصطناعي
Deck 7: Section 2: Applications of Integration
ملء الشاشة (f)
سؤال
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
, and 
about the 
-axis.
A)
B)
C)
D)
E)
, and about the -axis.A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
If the portion of the line 
lying in the first quadrant is revolved about the 
-axis, a cone is generated. Find the volume of the cone extending from 
. Round your answer to two decimal places.
A) 2929.33
B) 4601.39
C) 8788.00
D) 7362.22
E) 3497.05
lying in the first quadrant is revolved about the -axis, a cone is generated. Find the volume of the cone extending from . Round your answer to two decimal places.A) 2929.33
B) 4601.39
C) 8788.00
D) 7362.22
E) 3497.05
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the 
-axis. 
A)
B)
C)
D)
E)
-axis. A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, and 
about the line 
.
A)
B)
C)
D)
E)
, and about the line .A)
B)
C)
D)
E)
سؤال
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, and 
about the 
-axis. Round your answer to four decimal places.
A) 5.3098
B) 12.2824
C) 20.6444
D) 15.9387
E) 37.9232
, and about the -axis. Round your answer to four decimal places.A) 5.3098
B) 12.2824
C) 20.6444
D) 15.9387
E) 37.9232
سؤال
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
and 
in the first quadrant about the 
-axis.
A)
B)
C)
D)
E)
and in the first quadrant about the -axis.A)
B)
C)
D)
E)
سؤال
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
and 
about the 
-axis.
A)
B)
C)
D)
E)
and about the -axis.A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of 
and the x-axis 
about the x-axis, where x and y are measured in meters. Find the volume of the tank. Round your answer to two decimal places.
A) 0.45 m3
B) 0.33 m3
C) 0.03 m3
D) 1.79 m3
E) 0.12 m3
and the x-axis about the x-axis, where x and y are measured in meters. Find the volume of the tank. Round your answer to two decimal places.A) 0.45 m3
B) 0.33 m3
C) 0.03 m3
D) 1.79 m3
E) 0.12 m3
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the 
-axis. Verify your results using the integration capabilities of a graphing utility. 
A)
B)
C)
D)
E)
-axis. Verify your results using the integration capabilities of a graphing utility. A)
B)
C)
D)
E)
سؤال
The base of a solid is bounded by 
and 
. Find the volume of the solid if its cross-sections are squares (taken perpendicular to the 
-axis). Round your answer to two decimal places.
A) 57.60
B) 6.40
C) 70.40
D) 38.40
E) 25.60
and . Find the volume of the solid if its cross-sections are squares (taken perpendicular to the -axis). Round your answer to two decimal places.A) 57.60
B) 6.40
C) 70.40
D) 38.40
E) 25.60
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the 
-axis. 
A)
B)
C)
D)
E)
-axis. A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, and 
about the line 
.
A)
B)
C)
D)
E)
, and about the line .A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 7: Section 2: Applications of Integration
1
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by , and about the -axis.
A)
B)
C)
D)
E)
, and about the -axis.A)
B)
C)
D)
E)
2
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
3
If the portion of the line lying in the first quadrant is revolved about the -axis, a cone is generated. Find the volume of the cone extending from . Round your answer to two decimal places.
A) 2929.33
B) 4601.39
C) 8788.00
D) 7362.22
E) 3497.05
lying in the first quadrant is revolved about the -axis, a cone is generated. Find the volume of the cone extending from . Round your answer to two decimal places.A) 2929.33
B) 4601.39
C) 8788.00
D) 7362.22
E) 3497.05
4601.39
4
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the -axis.
A)
B)
C)
D)
E)
-axis. A)
B)
C)
D)
E)
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5
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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6
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , and about the line .
A)
B)
C)
D)
E)
, and about the line .A)
B)
C)
D)
E)
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7
A tank on a water tower is a sphere of radius 65 feet. Determine the depth of the water when the tank is filled to one-fourth of its total capacity. (Note: Use the zero or root feature of a graphing utility after evaluating the definite integral.) Round your answer to two decimal places.
A) 20.66 feet
B) 54.63 feet
C) 34.67 feet
D) 42.43 feet
E) 10.36 feet
A) 20.66 feet
B) 54.63 feet
C) 34.67 feet
D) 42.43 feet
E) 10.36 feet
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8
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , and about the -axis. Round your answer to four decimal places.
A) 5.3098
B) 12.2824
C) 20.6444
D) 15.9387
E) 37.9232
, and about the -axis. Round your answer to four decimal places.A) 5.3098
B) 12.2824
C) 20.6444
D) 15.9387
E) 37.9232
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9
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by and in the first quadrant about the -axis.
A)
B)
C)
D)
E)
and in the first quadrant about the -axis.A)
B)
C)
D)
E)
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10
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by and about the -axis.
A)
B)
C)
D)
E)
and about the -axis.A)
B)
C)
D)
E)
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11
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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12
A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of and the x-axis about the x-axis, where x and y are measured in meters. Find the volume of the tank. Round your answer to two decimal places.
A) 0.45 m3
B) 0.33 m3
C) 0.03 m3
D) 1.79 m3
E) 0.12 m3
and the x-axis about the x-axis, where x and y are measured in meters. Find the volume of the tank. Round your answer to two decimal places.A) 0.45 m3
B) 0.33 m3
C) 0.03 m3
D) 1.79 m3
E) 0.12 m3
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13
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the -axis. Verify your results using the integration capabilities of a graphing utility.
A)
B)
C)
D)
E)
-axis. Verify your results using the integration capabilities of a graphing utility. A)
B)
C)
D)
E)
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15
The base of a solid is bounded by and . Find the volume of the solid if its cross-sections are squares (taken perpendicular to the -axis). Round your answer to two decimal places.
A) 57.60
B) 6.40
C) 70.40
D) 38.40
E) 25.60
and . Find the volume of the solid if its cross-sections are squares (taken perpendicular to the -axis). Round your answer to two decimal places.A) 57.60
B) 6.40
C) 70.40
D) 38.40
E) 25.60
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16
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the -axis.
A)
B)
C)
D)
E)
-axis. A)
B)
C)
D)
E)
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18
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , and about the line .
A)
B)
C)
D)
E)
, and about the line .A)
B)
C)
D)
E)
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