Deck 7: Applications of Definite Integrals

Question 1

Find the volume of the described solid.

Answer 1

B

Question 2

Find the volume of the solid generated by revolving the shaded region about the given axis.

Answer 2

C

Question 3

Find the volume of the described solid.

Answer 3

D

Question 4

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 5

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 6

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 7

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 8

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 9

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 10

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 11

Find the volume of the described solid.

Question 12

Find the volume of the described solid.

Question 13

Find the volume of the described solid.

Question 14

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 15

Find the volume of the solid generated by revolving the shaded region about the given axis.

Question 16

Find the volume of the described solid.

Question 17

Find the volume of the described solid.

Question 18

Find the volume of the described solid.

A) 90
B) 18
C) 72
D) 144

Question 19

Find the volume of the described solid.

Question 20

Find the volume of the described solid.

Question 21

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 22

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 23

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 24

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 25

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 26

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 27

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 28

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
y = - 7x + 14, y = 7x, x = 0

Question 29

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 30

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 31

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 32

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
y = x, y = 0, x = 2, x = 4

Question 33

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
y = x + 2, y = 0, x = -2, x = 6

Question 34

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 35

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 36

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
y = 3x, y = 3, x = 0

Question 37

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 38

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 39

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 40

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 41

Find the volume of the solid generated by revolving the region about the y-axis.

Question 42

Find the volume of the solid generated by revolving the region about the y-axis.

Question 43

Find the volume of the solid generated by revolving the region about the given line.

Question 44

Find the volume of the solid generated by revolving the region about the y-axis.
The region enclosed by the triangle with vertices (0, 0), (4, 0), (4, 2)

Question 45

Find the volume of the solid generated by revolving the region about the y-axis.

Question 46

Find the volume of the solid generated by revolving the region about the y-axis.

Question 47

Find the volume of the solid generated by revolving the region about the given line.

Question 48

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.

Question 49

Find the volume of the solid generated by revolving the region about the y-axis.

Question 50

Find the volume of the solid generated by revolving the region about the given line.

Question 51

Find the volume of the solid generated by revolving the region about the given line.

Question 52

Find the volume of the solid generated by revolving the region about the given line.

Question 53

Find the volume of the solid generated by revolving the region about the given line.

Question 54

Find the volume of the solid generated by revolving the region about the y-axis.

Question 55

Find the volume of the solid generated by revolving the region about the given line.

Question 56

Find the volume of the solid generated by revolving the region about the given line.

Question 57

Find the volume of the solid generated by revolving the region about the y-axis.

Question 58

Find the volume of the solid generated by revolving the region about the y-axis.
The region enclosed by the triangle with vertices (1, 0), (1, 2), (3, 2)

Question 59

Find the volume of the solid generated by revolving the region about the given line.

Question 60

Find the volume of the solid generated by revolving the region about the given line.

Question 61

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 62

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 63

Find the volume of the solid generated by revolving the region about the y-axis.

Question 64

Solve the problem.
A frustum of a right circular cone has a height of 10 m, a base of radius 5m, and a top of radius 4m. Find its volume.

Question 65

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 66

Solve the problem.

Question 67

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 68

Solve the problem.
The hemispherical bowl of radius 5 contains water to a depth 3. Find the volume of water in the bowl.

Question 69

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 70

Solve the problem.
Find the volume that remains after a hole of radius 1 is bored through the center of a solid cylinder of radius 4 and height 8.

Question 71

Solve the problem.

A) 13
B) 4
C) 17
D) 7

Question 72

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 73

Solve the problem.

A) 38
B) 150
C) 75
D) 50

Question 74

Solve the problem.

Question 75

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 76

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 77

Solve the problem.

Question 78

Solve the problem.

Question 79

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

Question 80

Solve the problem.
Find the volume that remains after a hole of radius 1 is bored through the center of a solid sphere of radius 2. Round to the nearest tenth.

A) 5.4
B) 65.3
C) 6.9
D) 21.8