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Geometry & Spatial Sense – Practice Problems

Surface Area & Volume

1.

If the sphere shown above has a radius of 18 units, then what is the volume of the sphere?

A. 7,776 cubic units

B. 9,720 cubic units

C. 1,296 cubic units

D. 3,888 cubic units

Measurement Problems

2. Compute the following.

11 lb 6 oz - 8 lb 11 oz

A. 2 lb 5 oz

B. 3 lb 11 oz

C. 2 lb 11 oz

D. 3 lb 12 oz


3. Susie is pouring water into a tub. She pours 5 gallons, 5 cups, 8 pints, and 5 quarts of water

into the tub. How much water has Susie poured into the tub?

A. 126 cups

B. 62 cups

C. 81 cups

D. 121 cups

Similar Figures

4. Amanda is resizing a rectangular picture on her computer. The original picture has a width of

8 in and a length of 5 in. If she wants to keep it proportional, but have the new width be 4 in,

what should be the new length?

A. 10.0 in

B. 2.0 in

C. 7.5 in

D. 2.5 in

Properties of Polygons

5. Find the measure of one interior angle of a regular polygon with nine sides.

A. 280°

B. 70°

C. 1,260°

D. 140°

Geometric Patterns

6.

Look at Koch's Snowflake above. What would it look like after one more iteration?

W.

X.

Y.

Z.

A. Y

B. W

C. Z

D. X


7.

If X = 4 units, then what is the volume of the cube shown above?

A. 128 cubic units

B. 36 cubic units

C. 64 cubic units

D. 39 cubic units

Pythagorean Theorem

8.

*Note: Figure not drawn to scale.

If Y = 5 cm and Z = 13 cm, what is the length of X?

A. 12 cm

B. 9 cm

C. 13 cm

D. 11 cm

Object Transformations

9. Which of the following transformations will produce a figure that is similar, but not congruent,

to the original figure?

A. dilation

B. reflection

C. translation

D. rotation

Nets & Projective Views

10. Which of the four nets shown below can be folded into a triangular prism?

W.

X.

Y.

Z.

A. Z

B. Y

C. X

D. W

Geometric Patterns

11. Which of the following shapes show self-similarity?

W.

X.

Y.

Z.

A. X and Y

B. X and Z

C. X, Y, and Z

D. W and X

Geometric Patterns

12.

An oval-shaped pink bead is inserted next to each circle-shaped aqua bead in the necklace. Using

this new pattern, if a necklace is made with 120 beads, how many pattern segments will the

necklace have?

A. 21 with 4 left over

B. 20 with 2 left over

C. 20

D. 17


13.

The translation above shows an object moving ______________.

A. 8 units to the right and 3 units down

B. 8 units to the right and 2 units down

C. 9 units to the right and 3 units down

D. 9 units to the right and 2 units down


14. What is the main difference between a square and a rhombus?

A. A square has sides that are parallel, but a rhombus does not.

B. A rhombus is always bigger than a square.

C. A rhombus has 4 right angles, but a square does not.

D. A square must have 4 right angles, but a rhombus may or may not.

Pythagorean Theorem

15.

Is S = 7 cm and T = 24, what is the length of R?

A. 31 cm

B. 28 cm

C. 23 cm

D. 25 cm

Geometric Patterns

16. Determine the number of iterations that created the Koch's Snowflake below.

A. 2

B. 3

C. 1

D. 4

Geometric Patterns

17.

In the pattern sequence above there are five shapes. If this pattern is repeated for a total of 64

shapes, what would be the final shape?

A. hexagon

B. square

C. diamond

D. octagon


18. Find the measure of one interior angle of a regular octagon.

A. 270°

B. 1,080°

C. 135°

D. 180°

Perimeter & Area

19.

Note: Figure not drawn to scale.

If X = 7 units, Y = 13 units, and Z = 14 units, then what is the perimeter of the triangle shown

above?

A. 28 units

B. 33 units

C. 30 units

D. 34 units

Similar Figures

20.

Note: Figures are not drawn to scale.

Right triangle ABC is similar to right triangle DEF. If the measure of angle A is 33°, what is the

measure of angle F?

A. 147°

B. 57°

C. 33°

D. 89°

Similar Figures

21.

Note: Figures not drawn to scale.

In the picture above, KLMN ~ XYZW. If K = 8 m, L = 5 m, M = 7 m,

N = 13 m, and Z = 10.5 m, then what is the length of Y?

A. 19.5 m

B. 7.5 m

C. 12 m

D. 13.5 m

Geometric Patterns

22. At each iteration in the Sierpinski Triangle, the area of the original is changed by how much?

The first 3 iterations of Sierpinski's Triangle look like this:

A. increased by 75%

B. reduced by 50%

C. reduced by 25%

D. increased by 25%

Similar Figures

23.

Note: Figure is not drawn to scale.

The rectangle above has the dimensions 31 cm by 19 cm.

Which set of dimensions would produce a similar figure?

A. 31 cm by 95 cm

B. 165 cm by 95 cm

C. 155 cm by 19 cm

D. 155 cm by 95 cm

Pythagorean Theorem

24. The city of Nairobi, Kenya, is 470 km east and 185 km south of the city of Kampala,

Uganda. If Matunde is flying from Nairobi to Kampala, what is the shortest possible distance of

his flight? (Round to the nearest km.)

A. 505 km

B. 432 km

C. 655 km

D. 563 km

Perimeter & Area

25. A cylinder with a radius of 6 in, a height of 15 in, and its cross section are shown below.


What is the area of the cross section shown?

A.

B.

C.

D.

Geometric Patterns

26. The Iterated Function System (IFS)

A. is the result of geometric calculations.

B. includes a system to determine the area of a geometric figure.

C. is the means to stop geometric patterns from growing.

D. involves a simple transformation done to an object or shape that is repeatedly done on

resulting object or shape.

Perimeter & Area

27.

What is the approximate area of the figure above?

A. 12

B. 8 1/2

C. 15 1/2

D. 10


28. The vertices of a quadrilateral are located at (0, -2), (5, -2), (5, 6), and (0, 6).

Which of the following classifies this quadrilateral?

A. The quadrilateral is a square.

B. The quadrilateral is a trapezoid.

C. The quadrilateral is a rhombus.

D. The quadrilateral is a rectangle.


29. A 2-dimensional net is shown below.

Which of the following 3-dimensional shapes can be formed with this net?

A. rectangle

B. circle

C. cylinder

D. cone


30.

If the volume of the smaller cylinder is 36 in3, what is the volume of the larger cylinder?

(Volume = r2h)

A. 108 in3

B. 72 in3

C. 144 in3

D. 180 in3

Perimeter & Area

31.

16 units

9 units

What is the perimeter of the rectangle above?

A. 59 units

B. 25 units

C. 144 units

D. 50 units

Perimeter & Area

32.

If the area of the smaller rectangle is 30 inches2, what is the area of the larger rectangle?

A. 120 inches2

B. 90 inches2

C. 60 inches2

D. 240 inches2



4.997 kL - 5,396 cL

A. 399 cL

B. 5,391.003 cL

C. 494,304 cL

D. 4,896.3 cL

Pythagorean Theorem

34.


If Y = 8 ft and Z = 100 ft, what is the length of X?

A. 28 ft

B. 5 ft

C. 136 ft

D. 6 ft

Pythagorean Theorem

35.


If X = 9 cm and Y = 12 cm, what is the length of Z?

A. 15 cm

B. 13 cm

C. 14 cm

D. 18 cm


36.

Note: Figure not drawn to scale

If h = 15 units and r = 5 units, what is the volume of the cone shown above? Use 3.14 for .

A. 78.5 cubic units

B. 235.5 cubic units

C. 392.5 cubic units

D. 1,177.5 cubic units


37.


If l = 9 units, w = 8 units, and h = 17 units, what is the surface area of the rectangular prism

shown above?

A. 790 square units

B. 1,224 square units

C. 361 square units

D. 722 square units

Similar Figures

38. Rectangle ABDE and rectangle CDEF are similar.

What is the length of AE?

A.

B.

C.

D.

Perimeter & Area

39.

If the area of the smaller circle is 4 inches2, what is the area of the larger circle?

A. 8 inches2

B. 12 inches2

C. 16 inches2

D. 24 inches2

Geometric Patterns

40.

A necklace contains 100 beads. A section of it is shown above. If the pattern shown continues to

repeat itself in the necklace, how many circle-shaped aqua beads are in the necklace?

A. 90

B. 95

C. 19

D. 20


41.

Which graph shows a reflection across the x-axis?

A. IV

B. III

C. II

D. I


42.

Which solid is represented by the top, front, and side views above?

A. Z

B. W

C. Y

D. X


43. Paul is measuring pieces of wood in order to build a shelf. The first piece of wood measured

4 feet and 7 inches. The second piece of wood measures 2 feet and 5 inches. The third piece of

wood measures 2 feet and 8 inches. How much wood does Paul have altogether?

A. 9 feet 8 inches

B. 28 feet

C. 11 feet 2 inches

D. 7 feet 8 inches


44.

Lisa is drawing triangle STU that is a dilation from point (6,5) of triangle PQR. She has already

drawn points S and T.

At what coordinates should she plot point U, of triangle STU?

A. (6,-1)

B. (6,1)

C. (-3,-1)

D. (6,-4)


45. Jody juggled for 4 days and 6 hours. How many minutes did Jody juggle?

A. 420 minutes

B. 4.6 minutes

C. 6,120 minutes

D. 10 minutes

Pythagorean Theorem

46. Anthony was mapping out a route to ride his bike. The route he picked forms a right triangle,

as shown in the picture below.

If the route takes him 5 miles on Forrest Lane and 13 miles up Cedar Drive, how far will

Anthony ride down Pine Avenue?

A. 18 miles

B. 8 miles

C. 12 miles

D. 15 miles


47.

Which solid is represented by the front, side, and top views above?

A. Y

B. X

C. W

D. Z

Perimeter & Area

48.


If X = 13 units and h = 7 units, then what is the area of the triangle shown above?

A. 182 square units

B. 24.5 square units

C. 45.5 square units

D. 91 square units


49.

Which graph below shows a rotation of the object in the graph above about point (-2, 3)?

A. II

B. IV

C. I

D. III

Similar Figures

50.


The rectangle above has the dimensions 11 yd by 34 yd.


A. 87 yd by 238 yd

B. 11 yd by 238 yd

C. 77 yd by 34 yd

D. 77 yd by 238 yd



77.8 mg + 0.781 kg

A. 78.581 g

B. 78,581 g

C. 78.878 g

D. 781.0778 g


52. Which of the following is a quadrilateral that will always have 4 equal sides and 4 right

angles?

A. rectangle

B. trapezoid

C. rhombus

D. square

Pythagorean Theorem

53. Find the area of the right triangle pictured below.

*triangle not drawn to scale

12 in

11 in

A. 5.5 in2

B. 52.75 in2

C. 26.38 in2

D. 89.53 in2


54.


If l = 13 units, w = 8 units, and h = 4 units, what is the volume of the rectangular prism shown

above?

A. 832 cubic units

B. 416 cubic units

C. 376 cubic units

D. 208 cubic units


55.

Note: Figure is not drawn to scale

If x = 5 units, y = 6 units, z = 9 units, and h = 4 units, then what is the surface area of the

triangular prism shown above?

A. 168 units2

B. 192 units2

C. 96 units2

D. 105 units2

Perimeter & Area

56.

4 units

16 units

What is the area of the rectangle above?

A. 20 square units

B. 64 square units

C. 40 square units

D. 80 square units

Geometric Patterns

57. Which of the following shapes show self-similarity?

W.

X.

Y.

Z.

A. W, X, and Y

B. Y and Z

C. X, Y, and Z

D. X and Z

Similar Figures

58.


Triangles ABC and DEF are similar figures. If the length of side AC is 14 units, the length of

side BC is 8 units, and the length of side DF is 126 units, what is the length of side EF?

A. 63 units

B. 80 units

C. need more information

D. 72 units

Similar Figures

59.


In the picture above, KLMN ~ XYZW. If m K = 140°, m L = 109°, m M = 56°,

and m N = 55°, then what is the measure of W?

A. 109°

B. 56°

C. 132°

D. 55°

Perimeter & Area

60. The diagram shows isosceles triangle STU. Each vertex of triangle STU is a point on circle V.

If the area of circle V is sq units, what is the area of triangle STU?

A.

B.

C.

D.

Pythagorean Theorem

61.


If X = 5 cm and Y = 12 cm, what is the length of Z?

A. 13 cm

B. 12 cm

C. 10 cm

D. 11 cm


62.

The pictures above represent the front and side views of which of the objects below?

W.

X.

Y.

Z.

A. X

B. Y

C. W

D. Z

Similar Figures

63.


In the picture above, PQRST ~ VZYXW. If m P = 95°, m Q = 78°, m R = 224°, m S

= 36°, and m T = 107°, then what is the measure of W?

A. 224°

B. 107°

C. 78°

D. 36°

Pythagorean Theorem

64. Find the perimeter of the right triangle pictured below.

*triangle not drawn to scale

7 cm

25 cm

A. 56 cm

B. 26 cm

C. 58 cm

D. 84 cm


65.

Note: Figures are not drawn to scale

The pyramid and prism above have the same L, W, and H. The volume of the pyramid is 18 cm3.

What is the volume of the prism?

A. 36 cm3

B. 6 cm3

C. 12 cm3

D. 54 cm3


66. Alan is building a sign to put in front of his office building.

The sign has 6 sides.

The sign has 3 diagonals coming from each vertex.

The sum of the sign's interior angles equals 720°.

What shape is Alan's sign?

A. octagon

B. hexagon

C. pentagon

D. rectangle


67.

Which of the following describes the transformations performed on the object shown above?

A. The object was reflected across the x-axis and shifted 7 units in the x direction and -5 units

in the y direction.

B. The object was reflected across the y-axis and shifted 1 unit in the x direction and -7 units

in the y direction.

C. The object was reflected across the y-axis and shifted -1 unit in the x direction and -7 units

in the y direction.

D. The object was reflected across the x-axis and shifted 9 units in the x direction and -3 units

in the y direction.



5 ft 3 in + 7 ft 11 in

A. 11 ft 8 in

B. 12 ft 2 in

C. 13 ft 8 in

D. 13 ft 2 in


69.

W.

X.

Y.

Z.

Which of the objects above have the following front view?

A. X, Y, and Z

B. W and X

C. X and Y

D. W, X, and Y


70. The vertices of a quadrilateral are located at (-3, 2), (1, 5), (5, 2), and (1, -1).

Which of the following classifies this quadrilateral?

A. The quadrilateral is a rectangle.

B. The quadrilateral is a trapezoid.

C. The quadrilateral is a rhombus.

D. The quadrilateral is a square.


71. The drawing represents a 3-dimensional figure.

Which of the following represent the left and front views of the figure?

W.

X.

Y.

Z.

A. Z

B. X

C. W

D. Y


72.

The pictures above represent the front, side, and top views of which of the objects below?

W.

X.

Y.

Z.

A. Y

B. Z

C. W

D. X


73. Which of the four nets shown below can be formed into a cone?

W.

X.

Y.

Z.

A. X

B. Y

C. Z

D. W


74.


If x = 5 units and y = 9 units, then what is the volume of the square pyramid shown above?

A. 150 cubic units

B. 225 cubic units

C. 75 cubic units

D. 125 cubic units

Similar Figures

75.


The triangle above has side lengths of 30 mm and 38 mm.


A. 150 mm, 195 mm

B. 150 mm, 5 mm

C. 150 mm, 190 mm

D. 150 mm, 38 mm


76.

Which of the following shapes is shown above?

A. square

B. rectangle

C. trapezoid

D. parallelogram


77.

Which of the following set of pictures represents a side and the bottom view of this solid?

A.

B.

C.

D.

Similar Figures

78.


Rectangles ABCD and EFGH are similar figures because angles A, B, C, and D are congruent to

angles E, F, G, and H, respectively.

If DA equals 16 units, AB equals 7 units, and HE equals 112 units, what does EF equal?

A. 7 units

B. 256 units

C. 103 units

D. 49 units


79. Which of the four nets shown below can be folded into a triangular prism?

W.

X.

Y.

Z.

A. Z

B. Y

C. W

D. X


80. Find the measure of one interior angle of a regular pentagon.

A. 540°

B. 108°

C. 90°

D. 27°


81. Billy and his sister, Sarah, are competing to see who can throw their football the farthest.

Billy threw the football 32 yards. Sarah threw the football 1,136 inches. How much farther than

Sarah did Billy throw the football?

A. 97.6 inches

B. 23 inches

C. 16 inches

D. 20 inches


82.


Heights (Y and Z) have been rounded for computational ease.

If X = 4 units, Y = 3.5 units, and Z = 3.5 units, then what is the surface area of the right

triangular pyramid shown above?

A. 28 square units

B. 49 square units

C. 36 square units

D. 64 square units


83.

Find the sum of the interior angles of the polygon shown above.

A. 540°

B. 720°

C. 900°

D. 360°


84. The interior angles of a polygon equal 180°. How many sides does this polygon have?

A. 2

B. 4

C. 3

D. 5

Geometric Patterns

85.

If the 7-bead segment above is repeated several times to create a necklace with 70 beads, how

many oval-shaped beads will the necklace have?

A. 10

B. 30

C. 18

D. 20


86.

The translation above shows the object moving ______________.

A. 6 units to the left and 5 units up

B. 3 units to the left and 8 units up

C. 3 units to the right and 8 units down

D. 8 units to the right and 3 units down

Perimeter & Area

87.

7 in.

What is the circumference of the circle?

A. 21.98 in

B. 153.86 in

C. 43.96 in

D. 87.92 in



67.6 cm + 81 mm

A. 75.16 cm

B. 87.76 cm

C. 148.6 cm

D. 75.7 cm


89.


If W = 40 units, X = 28 units, Y = 50 units, and Z = 52 units, then what is the surface area of the

right rectangular pyramid shown above?

A. 4,576 units2

B. 8,032 units2

C. 2,848 units2

D. 3,456 units2

Geometric Patterns

90.

In the pattern above, how many blue dots will the diagram have in position 2?

A. 2

B. 3

C. 5

D. 4


91.

If the figure above was rotated 180° counter-clockwise about point A, where would point B on

the figure be plotted?

A. (0,-3)

B. (1,6)

C. (2,-3)

D. (6,2)

E. (6,1)


92. Which of the following transformations will always produce a congruent figure?

A. translation

B. enlargement

C. dilation

D. reduction


93.

The translation above shows an object moving ______________.

A. 5 units to the left and 7 units up

B. 7 units to the right and 5 units down

C. 5 units to the left and 7 units down

D. 5 units to the right and 7 units up

Pythagorean Theorem

94. The figure shows some of the dimensions of a parallelogram.


What is h, the height of the parallelogram?

A. 17 cm

B. 24 cm

C. 12 cm

D. 6 cm

Perimeter & Area

95.

What is the approximate area of the figure above?

A. 11

B. 12 1/2

C. 8

D. 9



2 c 5 fl oz + 5 c 6 fl oz

A. 8 c 7 fl oz

B. 7 c 3 fl oz

C. 8 c 3 fl oz

D. 8 c 9 fl oz


97. Parallelogram JKLM has the coordinates J (1, 8), K (11, 8), L (10, 2), and M (0, 2). Which of

the following sets of points represents a dilation from the origin of parallelogram JKLM?

A. J' (4, 8), K' (44, 8), L' (40, 2), M' (0, 2)

B. J' (5, 12), K' (15, 12), L' (14, 6), M' (4, 6)

C. J' (4, 32), K' (44, 32), L' (40, 8), M' (0, 8)

D. J' (1, 32), K' (44, 8), L' (40, 2), M' (0, 8)

Pythagorean Theorem

98. Benton has an extension ladder than can only be used at a length of 10 feet, 15 feet, or 20

feet. He places the base of the ladder 9 feet from the wall and needs the top of the ladder to reach

12 feet. Which ladder length would Benton need to use to reach this height on the wall?

A. 10 feet

B. 15 feet

C. 20 feet

D. None of these ladder lengths would reach this height.


99. A diver has 2,000 psi (pounds per square inch) in his dive tank at the beginning of a dive.

The end reading was 1,000 psi after a dive time of 15 minutes. At what rate was the pressure in

the dive tank decreasing?

A. 66.67 psi/min

B. 133.33 psi/min

C. 200 psi/min

D. |Round(10000*(a+c+e)/(b+d+d+1))/100| miles per hour

Pythagorean Theorem

100.

If L = 65 cm and J = 33 cm, what is the length of K?

A. 56 cm

B. 55 cm

C. 65 cm

D. 73 cm

Answers

1. A

2. C

3. D

4. D

5. D

6. C

7. C

8. A

9. A

10. B

11. A

12. C

13. D

14. D

15. D

16. C

17. D

18. C

19. D

20. B

21. B

22. C

23. D

24. A

25. A

26. D

27. A

28. D

29. C

30. C

31. D

32. A

33. C

34. D

35. A

36. C

37. D

38. C

39. C

40. D

41. D

42. D

43. A

44. A

45. C

46. C

47. D

48. C

49. B

50. D

51. D

52. D

53. C

54. B

55. A

56. B

57. B

58. D

59. D

60. A

61. A

62. A

63. B

64. A

65. D

66. B

67. C

68. D

69. D

70. C

71. A

72. C

73. C

74. C

75. C

76. D

77. D

78. D

79. D

80. B

81. C

82. A

83. A

84. C

85. D

86. B

87. C

88. D

89. A

90. B

91. E

92. A

93. A

94. C

95. A

96. C

97. C

98. B

99. A

100. A

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