Free Printable volume solid revolution

1.

All solids of revolution are:

a)

rectangular

b)

circular

c)

pyramids

d)

2D

2.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

3.

what is the volume of the cone formed by rotating this triangle about the x axis?

a)

113.04 u³

b)

339.12 u³

c)

169.56 u³

d)

56.52 u³

4.

what figure was rotated about the y axis to produce this cylinder?

a)

cylinder

b)

rectangle

c)

square

d)

triangle

5.

what is the volume of this cylinder?

a)

113.04 u³

b)

37.68 u³

c)

24 u³

d)

12 u³

6.

what figure is formed when this circle is rotated around the x axis?

a)

frustum

b)

circle

c)

sphere

d)

cylinder

7.

what common object would resemble this circle rotated around the x axis?

a)

ball

b)

can

c)

donut

d)

lamp

8.

if this 2D shape was rotated around the x axis, what common object would it resemble?

a)

box

b)

bowl

c)

pyramid

d)

triangle

9.

what 2 3D shapes would you break the solid of revolution into in order to find its volume?

a)

rectangle and trapezoid

b)

cone and prism

c)

pyramid and prism

d)

frustum and cylinder

10.

what is the volume of the cylinder formed when this figure is rotated about the x axis?

a)

1004.8 u³

b)

334.9 u³

c)

314 u³

d)

392.5 u³

11.

a)

A

b)

B

c)

C

12.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

13.

what figure was rotated about the y axis to produce this cylinder?

a)

cylinder

b)

rectangle

c)

square

d)

triangle

14.

what figure is formed when this circle is rotated around the x axis?

a)

frustum

b)

circle

c)

sphere

d)

cylinder

15.

if this 2D shape was rotated around the x axis, what common object would it resemble?

a)

box

b)

bowl

c)

pyramid

d)

triangle

16.

What is the volume of this solid of revolution?

a)

$\pi\int_2^8\ \left(x-2\right)^2dx$

b)

$\pi\int_2^8\ \left(x+2\right)^2dx$

c)

$\int_2^8\ \left(x-2\right)^2dx$

d)

$\pi\int_2^8\ \left(x+2\right)^{ }dx$

17.

What is the volume of this cylinder?

a)

$250\pi$

b)

$100\pi$ $\$

c)

$5\pi$

d)

$\frac{250}{3}\pi$

18.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

19.

Find the volume of the solid that results when the region enclosed by the equation $y=\sqrt{x+2}$ between x = 2 and x = 6 is revolved around the x-axis. Use pi for $\pi$ or round to 3 significant digits.

(a)

20.

Find the volume of the solid that results when the region enclosed by the equation $y=x^2+1$ is revolved around the x-axis between $x=-1$ and $x=2$ . Use pi for $\pi$ or round to 3 significant digits.

(a)

21.

Hint: Solve for x--you have to get rid of the ln using its inverse!

a)

b)

c)

d)

22.

a)

b)

c)

d)

23.

Use Geometry to evaluate the definite integral

a)

25

b)

51

c)

50

d)

49

24.

Find the area under the curve y =3x²-2x from x= 1 to x =5. Do not use your calculator.

a)

100

b)

99

c)

150

d)

152

25.

Find the area under the curve

a)

^17/5

b)

6/5

c)

13/3

d)

1/3

26.

Which definite integral models the area highlighted above?

a)

b)

c)

d)

27.

Using the areas of each region given
$\int_a^df\left(x\right)=$

a)

6

b)

20

c)

2

d)

24

28.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis.

a)

8π/3

b)

32π/5

c)

108π/5

d)

16π/3

29.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis.

a)

8π

b)

6π

c)

2π

d)

0

30.

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

a)

5.4

b)

30.6

c)

96.133

d)

108.332

31.

a)

A

b)

B

c)

C

d)

D

32.

What integral would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11.

a)

Bounds: [0, 2]; π ∫(4x⁴ - 8)dx

b)

Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx

c)

Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

d)

Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

33.

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

11π/3

b)

4π/13

c)

3π/7

d)

2π/5

34.

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, from x = 0 to x = π about the x-axis?

a)

π²

b)

π²/2

c)

4π²

d)

π/2

35.

What is the volume of the solid formed in the second quadrant bounded by the curves y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

a)

153π/2

b)

81π/2

c)

648π/5

d)

45π/2

36.

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated?

a)

72π/5

b)

27π/2

c)

27π/20

d)

9π/10

37.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

38.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

39.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

40.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

41.

a)

A

b)

B

c)

C

d)

D

e)

E

42.

a)

A

b)

B

c)

C

d)

D

e)

E

43.

a)

1/2

b)

2/3

c)

1

d)

2

44.

a)

12.566

b)

14.661

c)

16.755

d)

67.021

45.

a)

32pi/5

b)

16pi/3

c)

16pi/5

d)

8pi/3

46.

a)

3pi

b)

9pi/2

c)

9pi

d)

3pi/2

47.

Find the volume of the solid formed by revolving the region bounded by y = x and y = x²and the y-axis about the line y = 1.

a)

pi/4

b)

pi/5

c)

pi/3

d)

pi/2

48.

Write the integral that would be used to find the area bounded by y = x² + 1, y = x - 2, x = -2 and x = 2.

a)

b)

c)

d)

e)

49.

Write the integral that would be used to find the area of the region bounded by x = 1, y = √x and y = -x + 6.

a)

b)

c)

d)

e)

50.

Write the integral that would be used to find the area bounded by the graphs of x - y = 2, y = 8 and x = y^2/3.

a)

b)

c)

d)

e)

51.

Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

a)

b)

c)

d)

e)

52.

Find the area of the region bounded by the graphs of y = x² and y = 4x.

a)

32/3

b)

64/3

c)

32

d)

64

e)

32/5

53.

Find the area of the region bounded by the equations y = x² + 1 and y = 5.

a)

32/3

b)

64

c)

32

d)

64/3

e)

16

54.

Write the integral that would be used to find the volume of the region bounded by x = -1, x = 2, y = 0 and y = 1/2x² + 2.

a)

b)

c)

d)

e)

55.

Write the integral that would be used to find the volume of the solid obtained by revolving the region bounded by x = y² - 4, x = 0 and y = 0 about the y-axis.

a)

b)

c)

d)

e)

56.

Write the integral that can be used to find the volume of the solid obtained by revolving the region bounded by x = 3 and x = (25 - y²)^1/2 about the y axis.

a)

b)

c)

d)

e)

57.

Write the integral that could be used to find the volume of the solid formed when the region bounded by y = -2x² + 1 and y = -x² + 1 is revolved about the x-axis.

a)

b)

c)

d)

e)

58.

Write the integral that would be used to find the volume of the solid formed when the region bounded by y = (x - 2)^1/2, the x-axis and x = 11 is revolved about the y-axis.

a)

b)

c)

d)

e)

59.

Write the integral that would be used to find the volume of the solid generated when the region bounded by y = x² + 1, the x-axis, the y-axis and x = 3 is revolved about the y-axis.

a)

b)

c)

d)

e)

60.

Write the integral that would be used to find the volume of the solid generated when the region bounded by the x-axis, the y-axis and 2x + y = 6 is revolved about the x-axis.

a)

b)

c)

d)

e)

61.

Write the integral that would be used to find the volume of the solid generated when the region bounded by the graphs of the y-axis, x = 9 and y = x³ + 1 is revolved about the x-axis.

a)

b)

c)

d)

e)

62.

Select the formula for finding area under a curve bounded by the x axis.

a)

$\int_a^bf\left(x\right)dx$

b)

$\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx$

c)

$\int_a^b\left[f\left(x\right)\right]^2dx$

d)

$\pi\int_a^bf\left(x\right)dx$

63.

Find the integral for the area under the curve.

a)

$\int_{-6}^{-2}\ 2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

b)

$\int_{-6}^{-2}\ -2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

c)

$\int_{-6}^{-2}\ \left(x^2\ +\ 6x\ +\ 10\right)\ dx$

d)

$\int_{-6}^{-2}\ -4\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

64.

Find the integral that would find the area of the region enclosed by the curves.

a)

$\int_0^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

b)

$\int_1^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

c)

$\int_1^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

d)

$\int_0^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

65.

Select the formula(s) for find the volume of a solid of revolution around an axis using the disk method.

a)

$\pi\int_a^b\ f\left(x\right)^2\ dx$

b)

$\pi\int_a^b\ f\left(y\right)^2\ dy$

c)

$\pi\int_a^b\ f\left(x\right)^{ }dx$

d)

$\pi\int_a^b\ \ R\ dx$

66.

Select the formula(s) to find the volume of a solid of revolution using the washer method.

a)

$\pi\int_a^b\left[f\left(x\right)-g\left(x\right)\right]dx$

b)

$\pi\int_a^b\left[f\left(x\right)^2-g\left(x\right)^2\right]dx$

c)

$\pi\int_a^b\left[R^2-r^2\right]dx$

d)

$\pi\int_a^b\left[f\left(y\right)^2-g\left(y\right)^2\right]dy$

67.

If the region from (-1,0) is rotated about the x axis, would one use a washer or disk?

a)

washer

b)

disk

68.

If the region enclosed by these functions are revolved around the y axis, would one use a washer or disk?

a)

washer

b)

disk

69.

What is the outer radius (R) needed to find the volume of the region revolving around $y=1$ ?

a)

$1-\left(-x^2+6\right)$

b)

$\left(-x^2+6\right)-1$

c)

$2-1$

d)

$1-2$

70.

Select the integral that would find the volume of the region revolving around the given axis.

a)

b)

c)

d)

71.

Select the integral that would find the volume of the region revolving around the given axis.

a)

b)

c)

d)

72.

Find the area of the region

a)

b)

c)

d)

73.

Find the volume of the solid formed when cross sections perpendicular to the x axis are squares

a)

b)

c)

d)

74.

Find the volume of the solid formed when cross sections perpendicular to the x axis are semi-circles

a)

b)

c)

d)

75.

The region bounded by the line y = x and y = f(x) is rotated about the line y = k. Choose the correct representations of R and r

a)

R = k + f(x)

b)

R = k − f(x)

c)

r = k + x

d)

r = k − x

76.

The shaded region is bound by y = 2x, y = -2x, and y = x + 3. Choose two integrals that can be added to find the area of the shaded region.

a)

$\int_{-1}^0\ \left(x+3-2x\right)dx$

b)

$\int_{-1}^0\left(x\ +\ 3\ +\ 2x\right)dx$

c)

$\int_0^3\left(x+3-2x\right)dx$

d)

$\int_0^3\left(x+3\ +\ 2x\right)dx$

77.

Rectangle is rotated @ x-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

78.

Rectangle is rotated @ x-axis
Window $\left[\ -\ 2\ ,\ 10\ \right]\ x\ \left[\ -\ 1\ ,\ 8\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

79.

Rectangle is rotated @ y-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

80.

Rectangle is rotated @ y-axis
Window $\left[\ -\ 2\ ,\ 10\ \right]\ x\ \left[\ -\ 1\ ,\ 8\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

81.

Triangle is rotated @ x-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

82.

Triangle is rotated @ x-axis
Window $\left[\ -\ 2\ ,\ 10\ \right]\ x\ \left[\ -\ 4\ ,\ 20\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

83.

Triangle is rotated @ y-axis

Solid of revolution is the difference of 2 geometric figures

figure1 - figure 2

Submit figure1,figure2 (small letters)

(a)

84.

Triangle is rotated @ y-axis
Window $\left[\ -\ 2\ ,\ 10\ \right]\ x\ \left[\ -\ 4\ ,\ 20\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

85.

Trapezoid is rotated @ x-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

86.

Trapezoid is rotated @ x-axis
Window $\left[\ -\ 2\ ,\ 10\ \right]\ x\ \left[\ -\ 4\ ,\ 25\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

87.

Semicircle is rotated @ x-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

88.

Semicircle is rotated @ x-axis
Window $\left[\ -\ 10\ ,\ 10\ \right]\ x\ \left[\ -\ 4\ ,\ 8\ \right]$

Exact volume

A\cdot\pi

Submit

A

(a)

89.

CYLINDER
Volume
$\pi\ r^{\ A}\ h$

Submit $A$

(a)

90.

CONE
Volume
$\frac{A}{B}\ \pi\ r^{\ C}\ h$

Submit $A,B,C$

(a)

91.

SPHERE
Volume
$\frac{A}{B}\ \pi\ r^{\ C}$

Submit $A,B,C$

(a)

92.

FRUSTUM

(Circular Base)
Volume
$\frac{A}{B}\ \pi\ \left(C^2+C\cdot D+D^2\right)\ h$

Submit $A,B,C,D$

(a)

93.

If you were to find the volume of the solid created by revolving the region bounded by

y=\sqrt{x}

and

y=x^3

about the x-axis, which method should you use?

a)

Disk

b)

Washer

c)

Shell

d)

Washer or Shell

94.

If you were to find the volume of the solid created by revolving the region bounded by

y=2x^4-2x

and

y=\sin x

about the line y = -2, which method should you use?

a)

Disk

b)

Washer

c)

Shell

d)

Washer or Shell

95.

If you were to find the volume of the solid created by revolving the region bounded by

y=2x^4-2x

and

y=\sin x

about the line x= 5, which method should you use?

a)

Disk

b)

Washer

c)

Shell

d)

Washer or Shell

96.

If you were to find the volume of the solid created by revolving the region bounded by

y=2x^4-2x

and

y=\sin x

about the line x= 5 using the shell method, what would be your radius?

a)

x - 5

b)

x + 5

c)

5 - x

d)

5 + x

97.

If you were to find the volume of the solid created by revolving the region bounded by

y=2x^4-2x

and

y=\sin x

about the line x= 5 using the shell method, what would be your height?

a)

$\sin x-\left(2x^4-2x\right)$

b)

$\left(2x^4-2x\right)-\sin x$

c)

$\sin x$

d)

$2x^4-2x$

98.

Region P is the region bounded by the functions $y=x^2$ and y = 4 If you were to revolve this region around a given axis to find the volume of a solid, which axes would require you to use the washer method? (Select all that apply)

a)

x-axis

b)

y-axis

c)

x = 3

d)

y = -3

99.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis.

a)

8π/3

b)

32π/5

c)

108π/5

d)

16π/3

100.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis.

a)

8π

b)

6π

c)

2π

d)

0

101.

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

a)

5.4

b)

30.6

c)

96.133

d)

108.332

102.

What integral would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11.

a)

Bounds: [0, 2]; π ∫(4x⁴ - 8)dx

b)

Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx

c)

Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

d)

Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

103.

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

11π/3

b)

4π/13

c)

3π/7

d)

2π/5

104.

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

11π/3

b)

4π/13

c)

3π/7

d)

2π/5

105.

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, from x = 0 to x = π about the x-axis?

a)

π²

b)

π²/2

c)

4π²

d)

π/2

106.

What is the volume of the solid formed in the second quadrant bounded by the curves y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

a)

153π/2

b)

81π/2

c)

648π/5

d)

45π/2

107.

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated?

a)

72π/5

b)

27π/2

c)

27π/20

d)

9π/10

108.

What is the volume of this solid of revolution?

a)

$\pi\int_2^8\ \left(x-2\right)^2dx$

b)

$\pi\int_2^8\ \left(x+2\right)^2dx$

c)

$\int_2^8\ \left(x-2\right)^2dx$

d)

$\pi\int_2^8\ \left(x+2\right)^{ }dx$

109.

Select the formula for finding area under a curve bounded by the x axis.

a)

$\int_a^bf\left(x\right)dx$

b)

$\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx$

c)

$\int_a^b\left[f\left(x\right)\right]^2dx$

d)

$\pi\int_a^bf\left(x\right)dx$

110.

Find the integral for the area under the curve.

a)

$\int_{-6}^{-2}\ 2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

b)

$\int_{-6}^{-2}\ -2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

c)

$\int_{-6}^{-2}\ \left(x^2\ +\ 6x\ +\ 10\right)\ dx$

d)

$\int_{-6}^{-2}\ -4\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

111.

Find the integral that would find the area of the region enclosed by the curves.

a)

$\int_0^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

b)

$\int_1^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

c)

$\int_1^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

d)

$\int_0^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

112.

Select the formula(s) for find the volume of a solid of revolution around an axis using the disk method.

a)

$\pi\int_a^b\ f\left(x\right)^2\ dx$

b)

$\pi\int_a^b\ f\left(y\right)^2\ dy$

c)

$\pi\int_a^b\ f\left(x\right)^{ }dx$

d)

$\pi\int_a^b\ \ R\ dx$

113.

What is the volume of this cylinder?

a)

$250\pi$

b)

$100\pi$ $\$

c)

$5\pi$

d)

$\frac{250}{3}\pi$

114.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

115.

a)

A

b)

B

c)

C

d)

D

116.

a)

A

b)

B

c)

C

d)

D

117.

Find the area of the region bounded by the equations y = x² + 1 and y = 5.

a)

32/3

b)

64

c)

32

d)

64/3

e)

16

118.

a)

A

b)

B

c)

C

d)

D

119.

Which integral best represents the volume of revolution when the shaded area is rotated 2 $\pi$ radians about the y-axis.

a)

$\pi\int_0^3\left(x-3\right)dx$

b)

$\pi\int_0^3y^2dy$

c)

$\pi\int_0^{\sqrt{2}}y^2+3\ dy$

d)

$\pi\int_0^{\sqrt{2}}\left(y^2+3\right)^2\ dy$

120.

Which integral best represents the volume of revolution when the shaded area is rotated 2π radians about the x-axis.

a)

$\pi\int_1^{e^3}\left(\frac{1}{3}\ln y\right)^2dy$

b)

$\pi\int_0^1\left(e^3-e^{3x}\right)dx$

c)

$\pi\int_0^1\left(e^3-e^{3x}\right)^2dx$

d)

$\pi e^6-\pi\int_0^1e^{6x}dx$

121.

a)

b)

c)

d)

122.

a)

b)

c)

d)

123.

a)

b)

c)

d)

124.

Which one of the definite integrals below gives the volume of the solid?

a)

$\pi\int_0^3e^{2y}dy$

b)

$\pi\int_0^3\left[\ln\left(y\right)\right]^2dy$

c)

$\pi\int_0^{\ln3}e^{2y}dy$

d)

$\pi\int_0^{e^3}\left[\ln\left(y\right)\right]^2dy$

125.

Write the integral that would be used to find the volume of the solid obtained by revolving the region bounded by x = y² - 4, x = 0 and y = 0 about the y-axis.

a)

b)

c)

d)

e)

126.

Write the integral that would be used to find the volume of the solid generated when the region bounded by the x-axis, the y-axis and 2x + y = 6 is revolved about the x-axis.

a)

b)

c)

d)

e)

127.

Write the integral that would be used to find the volume of the solid generated when the region bounded by y = x² + 1, the x-axis, the y-axis and x = 3 is revolved about the y-axis.

a)

b)

c)

d)

e)

128.

Find the volume of the region that revolves around the x axis.

a)

b)

c)

d)

129.

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

a)

5.4

b)

30.6

c)

96.133

d)

108.332

130.

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

11π/3

b)

4π/13

c)

3π/7

d)

2π/5

131.

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated?

a)

72π/5

b)

27π/2

c)

27π/20

d)

9π/10

132.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

133.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

134.

Set up but do not solve an integral that will find the volume of the solid described.

a)

A

b)

B

c)

C

d)

D

e)

E

135.

What is the volume of this solid of revolution?

a)

$\pi\int_2^8\ \left(x-2\right)^2dx$

b)

$\pi\int_2^8\ \left(x+2\right)^2dx$

c)

$\int_2^8\ \left(x-2\right)^2dx$

d)

$\pi\int_2^8\ \left(x+2\right)^{ }dx$

136.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis.

a)

8π

b)

6π

c)

2π

d)

0

137.

a)

b)

c)

d)

138.

a)

A

b)

B

c)

C

d)

D

139.

Select the formula for finding area under a curve bounded by the x axis.

a)

$\int_a^bf\left(x\right)dx$

b)

$\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx$

c)

$\int_a^b\left[f\left(x\right)\right]^2dx$

d)

$\pi\int_a^bf\left(x\right)dx$

140.

Select the formula(s) to find the volume of a solid of revolution using the washer method.

a)

$\pi\int_a^b\left[f\left(x\right)-g\left(x\right)\right]dx$

b)

$\pi\int_a^b\left[f\left(x\right)^2-g\left(x\right)^2\right]dx$

c)

$\pi\int_a^b\left[R^2-r^2\right]dx$

d)

$\pi\int_a^b\left[f\left(y\right)^2-g\left(y\right)^2\right]dy$

141.

Select the integral that would find the volume of the region revolving around the given axis.

a)

b)

c)

d)

142.

Find the area of the region

a)

b)

c)

d)

143.

Which one of the definite integrals below gives the volume of the solid?

a)

$\pi\int_0^3e^{2y}dy$

b)

$\pi\int_0^3\left[\ln\left(y\right)\right]^2dy$

c)

$\pi\int_0^{\ln3}e^{2y}dy$

d)

$\pi\int_0^{e^3}\left[\ln\left(y\right)\right]^2dy$

144.

Which one of the definite integrals gives the volume of the solid?

a)

$\pi\int_1^4\left[e^y+4\right]^2dy$

b)

$\pi\int_1^4\left[\ln\left(y\right)-4\right]dy$

c)

$\pi\int_1^4\left[\ln\left(y\right)+4\right]^2dy$

d)

$\pi\int_1^4\left[e^y-4\right]^2dy$

145.

Find the volume of the region that revolves around the y axis.

a)

b)

c)

d)

146.

CHALLENGE: Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

$\frac{11\pi}{3}$

b)

$\frac{4\pi}{13}$

c)

$\frac{3\pi}{7}$

d)

$\frac{2\pi}{5}$

147.

The straight line y = mx + 14 is a tangent to the curve $y=\frac{12}{x}+2$
at the point P. Find the value of the constant m and the coordinates of P

a)

m = 3 and y = - 8

b)

m = −3 and y = 8

c)

m = 8 and y = - 3

d)

m = −8 and y = 3

148.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

149.

What were the children served on the train in polar express?

a)

pizza

b)

hot cocoa

c)

chocolate bars

150.

1. Where is the whole family planning to travel to in Home Alone?

a)

a. Chicago

b)

b. Paris

c)

c. Ohio

d)

d. Miami

151.

Find the volume of the solid that results when the region enclosed by the equation $y=\sqrt{x+2}$ between x = 2 and x = 6 is revolved around the x-axis. Use pi for $\pi$ or round to 3 significant digits.

(a)

152.

Find the volume of the solid that results when the region enclosed by the equation $y=-x^2+1$ is revolved around the x-axis. Use pi for $\pi$ or round to 3 significant digits.

(a)

153.

Find the volume of the solid that results when the region enclosed by the equation $y=x^2+1$ is revolved around the x-axis between $x=-1$ and $x=2$ . Use pi for $\pi$ or round to 3 significant digits.

(a)

154.

Find the volume of the solid that results when the region enclosed by the equation $y=\frac{1}{x}$ is revolved around the x-axis between $x=\frac{1}{4}$ and $x=2$ . Use pi for $\pi$ or round to 3 significant digits.

(a)

155.

Find the volume of the solid that results when the region enclosed by the equation $y=x^2+2$ is revolved around the x-axis between $x=1$ and $x=2$ . Use pi for $\pi$ or round to 3 significant digits.

(a)

156.

Find the volume of the solid that results when the region enclosed by the equation $y=^3\sqrt{x}$ is revolved around the x-axis between $x=0$ and $x=1$ . Use pi for $\pi$ or round to 3 significant digits.

(a)

157.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

158.

a)

A

b)

B

c)

C

159.

what figure was rotated about the y axis to produce this cylinder?

a)

cylinder

b)

rectangle

c)

square

d)

triangle

160.

What is the volume of this solid of revolution?

a)

$\pi\int_2^8\ \left(x-2\right)^2dx$

b)

$\pi\int_2^8\ \left(x+2\right)^2dx$

c)

$\int_2^8\ \left(x-2\right)^2dx$

d)

$\pi\int_2^8\ \left(x+2\right)^{ }dx$

161.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the y-axis.

a)

8π

b)

6π

c)

2π

d)

0

162.

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² and the x-axis from [0, 2] around the x-axis.

a)

8π/3

b)

32π/5

c)

108π/5

d)

16π/3

163.

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

a)

5.4

b)

30.6

c)

96.133

d)

108.332

164.

The base of a solid is the region in the first quadrant enclosed by the parabola 𝑦 = 4𝑥² , the line 𝑥 = 1, and the 𝑥-axis. Each plane section of the solid perpendicular to the 𝑥-axis is a square. The volume of the solid is…

a)

4/3

b)

16/5

c)

4

d)

16

165.

The base of a solid is the region in the first quadrant enclosed by the graph of 𝑦 = 2 − 𝑥² and the coordinate axes. If every cross section of the solid perpendicular to the 𝑦-axis is a square, the volume of the solid is given by...

a)

$\int_0^2\left(2-x^2\right)^2dx$

b)

$\int_0^2\sqrt{2-y}dy$

c)

$\int_0^2\left(2-y\right)dy$

d)

$\int_0^2\left(2-x^2\right)dx$

166.

Find the volume of the solid that results when the region enclosed by the equation $y=\sqrt{x-6}$

between x = 6 and x = 10 is revolved around the x-axis.

Use pi for π

(a)

167.

Use the disk/washer method

a)

B

b)

C

c)

D

d)

E

168.

What is the volume of the solid formed in the second quadrant bounded by the curves y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

a)

153π/2

b)

81π/2

c)

648π/5

d)

45π/2

169.

The base of a solid is the region enclosed between the graphs of y=sinx and y=-sinx from x=0 to x= $\pi$ . Each cross section perpendicular to the x-axis is a semicircle with diameter connecting the two graphs. Find the volume of the solid.

a)

$\frac{\pi^2}{8}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi^2}{4}$

d)

$\frac{2\pi^2}{3}$

170.

Find the volume of the figure formed when the region bounded by $y=e^x$ for $1\le y\le5$ has cross-sections perpendicular to y that are rectangles, with a height 3 times that of the base. (Calculator active)

a)

.133

b)

,891

c)

14.571

d)

,283

171.

Calculate the Volume

a)

410 cm3

b)

420 cm3

c)

402 cm3

d)

401 cm3

172.

Choir is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches.

Which equation can be used to find the volume of the container?

a)

V = π(9)

b)

V = π(4.5)²(32)

c)

V = π(9)²(32)

d)

V = π(4.5)(32)

173.

Find the volume of the following cone.

a)

489.84 m³

b)

2204.28 m³

c)

6612.84 m³

d)

244.92 m³

174.

Find the volume of the figure. Round to the nearest whole number.

a)

317 units³

b)

635 units³

c)

1,904 units³

d)

890 units³

175.

Find the volume of the solid shown.

a)

4188.79 mm³

b)

523.599 mm³

c)

418.879 mm³

d)

104.72 mm³

176.

if this triangle is rotated about the x axis, what figure is formed?

a)

pyramid

b)

cylinder

c)

cone

d)

frustum

177.

what figure was rotated about the y axis to produce this cylinder?

a)

cylinder

b)

rectangle

c)

square

d)

triangle

178.

what figure is formed when this circle is rotated around the x axis?

a)

frustum

b)

circle

c)

sphere

d)

cylinder

179.

if this 2D shape was rotated around the x axis, what common object would it resemble?

a)

box

b)

bowl

c)

pyramid

d)

triangle

180.

Trapezoid is rotated @ x-axis

What geometric figure is formed?

Submit 1 word (small letters)

(a)

181.

A cone is cut by a plane that is perpendicular to its base. Which of the following could be the shape of the cross-section formed?

a)

Circle

b)

Triangle

c)

Rectangle

d)

Trapezoid

182.

If you cut a cylinder perpendicular to its bases, what shape will you get?

a)

A Circle

b)

A Triangle

c)

A Square

d)

A Rectangle

183.

What 3-D solid is formed when this rectangle is rotated about the vertical line?

a)

Right, rectangular prism

b)

Right, circular cylinder

c)

Right, oval cylinder

d)

Right, square prism

184.

Describe the cross section.

a)

rectangle

b)

square

c)

oval

d)

circle

185.

A right hexagonal prism is shown below. A two-dimensional cross section that is perpendicular to the base is taken from the prism.

Which figure describes the two-dimensional cross section?

a)

triangle

b)

rectangle

c)

pentagon

d)

hexagon

186.

The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a

a)

circle

b)

square

c)

triangle

d)

rectangle

187.

Rotating this rectangle around line BD create a cylinder with:

a)

height 15 and radius 8

b)

height 15 and radius 4

c)

height 8 and radius 15

d)

height 8 and radius 7.5

188.

A object has a volume of 17 mL. The same object has a mass of 212 g. What is the density of this object?

a)

12.4 g/m3

b)

12.4 g/mL

c)

1.24 g/mL

d)

12/4 mL/g

189.

The density of this material is 2 g/cm³.
There are 24 cm³ Find the total mass.

a)

12 grams

b)

48 grams

c)

12 g/cm³

d)

48 g/cm³

190.

If you have a gold brick that is 2 cm by 3 cm by 4 cm and has a density of 19.3 g/cm³, what is its mass?

a)

463.2 g/cm³

b)

463.2 g

c)

0.804 kg

d)

0.804 g

volume solid revolution

Total questions: 190

Worksheet time: 12hrs 43mins

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