Deck 7: Section 3: Applications of Integration

Question 1

A solid is generated by revolving the region bounded by and about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. Find the diameter of the hole. Round your answer to three decimal places.

A) 10.733
B) 11.167
C) 4.392
D) 2.536
E) 8.785

Answer 1

8.785

Question 2

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

A)
B)
C)
D)
E)

Answer 2

Question 3

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by about the x-axis.

A)
B)
C)
D)
E)

Answer 3

Question 4

Use the disk or shell method to 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)

Question 5

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

A)
B)
C)
D)
E)

Question 6

Use the disk or shell method to 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)

Question 7

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A)
B)
C)
D)
E)

Question 8

Use the shell method to find the volume of the solid generated by revolving the plane region about the line .

A)
B)
C)
D)
E)

Question 9

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Round your answer to two decimal places.

A) 674.33
B) 17.75
C) 96.05
D) 301.76
E) 453.96

Question 10

Use the shell method to find the volume of the solid generated by revolving the plane region bounded by about the line .

A)
B)
C)
D)
E)

Question 11

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A)
B)
C)
D)
E)

Question 12

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A)
B)
C)
D)
E)

Question 13

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by about the y-axis. Round your answer to three decimal places.

A) 5.987
B) 0.561
C) 2.047
D) 0.972
E) 2.917

Question 14

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

A)
B)
C)
D)
E)

Question 15

A solid is generated by revolving the region bounded by and about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-third of the volume is removed. Find the diameter of the hole. Round your answer to three decimal places.

A) 11.547
B) 5.774
C) 4.867
D) 18.838
E) 9.734

Question 16

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. (i) the x-axis; (ii) the y-axis

A)
B)
C)
D)
E)

Question 17

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

A)
B)
C)
D)
E)